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class="infobox-above" style="font-size:125%;"><div class="fn">James Edward Humphreys</div></th></tr><tr><th scope="row" class="infobox-label">Born</th><td class="infobox-data"><span style="display:none">(<span class="bday">1939-12-10</span>)</span>December 10, 1939<br /><div style="display:inline" class="birthplace"><a href="/wiki/Erie,_Pennsylvania" title="Erie, Pennsylvania">Erie, Pennsylvania</a>, U.S.</div></td></tr><tr><th scope="row" class="infobox-label">Died</th><td class="infobox-data">August 27, 2020<span style="display:none">(2020-08-27)</span> (aged 80)<br /><div style="display:inline" class="deathplace"><a href="/wiki/Leeds,_Massachusetts" title="Leeds, Massachusetts">Leeds, Massachusetts</a>, U.S.</div></td></tr><tr><th scope="row" class="infobox-label">Education</th><td class="infobox-data">Bachelor's degree from <a href="/wiki/Oberlin_College" title="Oberlin College">Oberlin College</a> (1961), master's degree from <a href="/wiki/Yale_University" title="Yale University">Yale University</a> (1964), PhD from Yale University (1966)</td></tr><tr><th scope="row" class="infobox-label">Occupation</th><td class="infobox-data role">Mathematician</td></tr><tr><th scope="row" class="infobox-label">Known for</th><td class="infobox-data">Writing <i>Introduction to Lie Algebras and Representation Theory</i><br />Receiving the <a href="/wiki/Lester_R._Ford_Award" class="mw-redirect" title="Lester R. Ford Award">Lester R. Ford Award</a> in 1976</td></tr></tbody></table> <p><b>James Edward Humphreys</b> (December 10, 1939 – August 27, 2020) was an American mathematician who worked in <a href="/wiki/Algebraic_group" title="Algebraic group">algebraic groups</a>, <a href="/wiki/Lie_group" title="Lie group">Lie groups</a>, and <a href="/wiki/Lie_algebra" title="Lie algebra">Lie algebras</a> and applications of these mathematical structures. He is known as the author of several mathematical texts, such as <i>Introduction to Lie Algebras and Representation Theory</i><sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> and <i>Reflection Groups and Coxeter Groups</i>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>After contracting <a href="/wiki/COVID-19" title="COVID-19">COVID-19</a> weeks earlier during the <a href="/wiki/COVID-19_pandemic_in_Massachusetts" title="COVID-19 pandemic in Massachusetts">COVID-19 pandemic in Massachusetts</a>, Humphreys died on August 27, 2020, at the age of 80.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Education">Education</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=James_E._Humphreys&action=edit&section=1" title="Edit section: Education"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Humphreys attended elementary and secondary school in Erie, Pennsylvania and then studied at <a href="/wiki/Oberlin_College" title="Oberlin College">Oberlin College</a> (bachelor's degree 1961) and from 1961 philosophy and mathematics at <a href="/wiki/Cornell_University" title="Cornell University">Cornell University</a>. At <a href="/wiki/Yale_University" title="Yale University">Yale University</a> he earned his master's degree in 1964 and his PhD in 1966 under <a href="/wiki/George_Seligman" title="George Seligman">George Seligman</a> with thesis <i>Algebraic Lie Algebras over fields of prime characteristic</i>.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Career">Career</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=James_E._Humphreys&action=edit&section=2" title="Edit section: Career"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In 1966, he became an assistant professor at the <a href="/wiki/University_of_Oregon" title="University of Oregon">University of Oregon</a> and in 1970, an associate professor at <a href="/wiki/New_York_University" title="New York University">New York University</a>. At the <a href="/wiki/University_of_Massachusetts_Amherst" title="University of Massachusetts Amherst">University of Massachusetts Amherst</a> he became in 1974 an associate professor and in 1976 a full professor; he retired there in 2003 as professor emeritus. In 1968/69 and in 1977, he was a visiting scholar at the <a href="/wiki/Institute_for_Advanced_Study" title="Institute for Advanced Study">Institute for Advanced Study</a><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> and in 1969/70 at the <a href="/wiki/Courant_Institute_of_Mathematical_Sciences" title="Courant Institute of Mathematical Sciences">Courant Institute of Mathematical Sciences</a> of New York University. In 1985, he was a visiting professor at <a href="/wiki/Rutgers_University" title="Rutgers University">Rutgers University</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Works">Works</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=James_E._Humphreys&action=edit&section=3" title="Edit section: Works"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Arithmetic Groups, <a href="/wiki/Lecture_Notes_in_Mathematics" title="Lecture Notes in Mathematics">Lecture Notes in Mathematics</a> 789, Springer Verlag 1980 (from lectures at the Courant Institute 1971)</li> <li><a rel="nofollow" class="external text" href="https://books.google.com/books/about/Conjugacy_Classes_in_Semisimple_Algebrai.html?id=m8h9iXRRaPAC">Conjugacy classes in semisimple algebraic groups</a>, AMS 1995<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li> <li><a rel="nofollow" class="external text" href="https://books.google.com/books/about/Introduction_to_Lie_Algebras_and_Represe.html?id=mSD4DvUFa6QC">Introduction to Lie Algebras and Representation Theory</a>, Springer Verlag, <a href="/wiki/Graduate_Texts_in_Mathematics" title="Graduate Texts in Mathematics">Graduate Texts in Mathematics</a>, 1972, 7th edition 1997 (also translated into Chinese and Russian)</li> <li>Linear Algebraic Groups, Graduate Texts in Mathematics, <a href="/wiki/Springer_Science%2BBusiness_Media" title="Springer Science+Business Media">Springer Verlag</a> 1974, 1998 (also translated into Russian). <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output 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text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0396773">0396773</a></li> <li>Ordinary and modular representations of Chevalley groups, Springer Verlag 1976. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=0453884">0453884</a></li> <li>Modular representations of finite groups of Lie type, London Mathematical Society Lecture Note Series 326, <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a> 2006<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup></li> <li><a rel="nofollow" class="external text" href="https://books.google.com/books/about/Reflection_Groups_and_Coxeter_Groups.html?id=ODfjmOeNLMUC">Reflection Groups and Coxeter Groups</a>, <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a> 1990. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1066460">1066460</a></li> <li><a rel="nofollow" class="external text" href="https://books.google.com/books/about/Representations_of_Semisimple_Lie_Algebr.html?id=8GCP4Ng6risC">Representations of semisimple Lie algebras in the BGG category <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {O}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {O}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6ae2ed4058fb748a183d9ada8aea50a00d0c89f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.85ex; height:2.176ex;" alt="{\displaystyle {\mathcal {O}}}"></span></a>, AMS 2008<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup></li> <li>Modular representations of simple Lie algebras, Bull. Amer. Math. Soc. (N.S.), Vol. 35, 1998, pp. 105–122. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1090%2FS0273-0979-98-00749-6">10.1090/S0273-0979-98-00749-6</a></li> <li>Modular representations of classical Lie algebras, Bull. Amer. Math. Soc., Vol. 76, 1970, 878–882 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1090%2FS0002-9904-1970-12594-0">10.1090/S0002-9904-1970-12594-0</a></li> <li><a rel="nofollow" class="external text" href="https://www.ams.org/books/memo/0071/"><i>Algebraic groups and modular Lie algebras</i></a>, Memoirs AMS 71, 1967</li> <li>Hilbert's fourteenth problem, <a href="/wiki/American_Mathematical_Monthly" class="mw-redirect" title="American Mathematical Monthly">American Mathematical Monthly</a>, Vol. 85, 1978, 341–353</li> <li>Representations of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {SL} (2,p)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>SL</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {SL} (2,p)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bd7e15cc7e6aac551139d2a57983db07a92b544" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.92ex; height:2.843ex;" alt="{\displaystyle \operatorname {SL} (2,p)}"></span>, Amer. Math. Monthly, Vol. 82, 1975, 21–39</li> <li>Highest weight modules for semisimple Lie algebras, in: Representation Theory I, <a href="/wiki/Lecture_Notes_in_Mathematics" title="Lecture Notes in Mathematics">Lecture Notes in Mathematics</a> 831, Springer Verlag 1980, pp, 72–103 <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBFb0089779">10.1007/BFb0089779</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Awards">Awards</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=James_E._Humphreys&action=edit&section=4" title="Edit section: Awards"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Humphreys received the <a href="/wiki/Lester_R._Ford_Award" class="mw-redirect" title="Lester R. Ford Award">Lester R. Ford Award</a> for the publication <i>Representations of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {SL} (2,p)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>SL</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {SL} (2,p)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bd7e15cc7e6aac551139d2a57983db07a92b544" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.92ex; height:2.843ex;" alt="{\displaystyle \operatorname {SL} (2,p)}"></span></i> in 1976.<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=James_E._Humphreys&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.maa.org/publications/maa-reviews/introduction-to-lie-algebras-and-representation-theory">"Review: Introduction to Lie Algebras and Representation Theory"</a>. <i>MAA Reviews</i>. December 31, 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=MAA+Reviews&rft.atitle=Review%3A+Introduction+to+Lie+Algebras+and+Representation+Theory&rft.date=2012-12-31&rft_id=http%3A%2F%2Fwww.maa.org%2Fpublications%2Fmaa-reviews%2Fintroduction-to-lie-algebras-and-representation-theory&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJames+E.+Humphreys" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHumphreys1990" class="citation book cs1">Humphreys, James E. (1990). <a rel="nofollow" class="external text" href="https://www.cambridge.org/core/books/reflection-groups-and-coxeter-groups/2910C1E00877D33A04A512791B6EDD72"><i>Reflection Groups and Coxeter Groups</i></a>. Cambridge University Press. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1017%2FCBO9780511623646">10.1017/CBO9780511623646</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780521375108" title="Special:BookSources/9780521375108"><bdi>9780521375108</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Reflection+Groups+and+Coxeter+Groups&rft.pub=Cambridge+University+Press&rft.date=1990&rft_id=info%3Adoi%2F10.1017%2FCBO9780511623646&rft.isbn=9780521375108&rft.aulast=Humphreys&rft.aufirst=James+E.&rft_id=https%3A%2F%2Fwww.cambridge.org%2Fcore%2Fbooks%2Freflection-groups-and-coxeter-groups%2F2910C1E00877D33A04A512791B6EDD72&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJames+E.+Humphreys" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.legacy.com/obituaries/erietimesnews/obituary.aspx?n=james-e-humphreys&pid=196925399">"James E. Humphreys (obituary)"</a>. <i>Erie Times-News</i>. October 10, 2020<span class="reference-accessdate">. Retrieved <span class="nowrap">November 12,</span> 2020</span> – via Legacy.com.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Erie+Times-News&rft.atitle=James+E.+Humphreys+%28obituary%29&rft.date=2020-10-10&rft_id=https%3A%2F%2Fwww.legacy.com%2Fobituaries%2Ferietimesnews%2Fobituary.aspx%3Fn%3Djames-e-humphreys%26pid%3D196925399&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJames+E.+Humphreys" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://mathgenealogy.org/id.php?id=26472">James E. Humphreys</a> at the <a href="/wiki/Mathematics_Genealogy_Project" title="Mathematics Genealogy Project">Mathematics Genealogy Project</a></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.ias.edu/people/cos/users/4762">"Humphreys, James E."</a> <i>ias.edu</i><span class="reference-accessdate">. Retrieved <span class="nowrap">January 28,</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=ias.edu&rft.atitle=Humphreys%2C+James+E.&rft_id=https%3A%2F%2Fwww.ias.edu%2Fpeople%2Fcos%2Fusers%2F4762&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJames+E.+Humphreys" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFProcesi1997" class="citation journal cs1"><a href="/wiki/Claudio_Procesi" title="Claudio Procesi">Procesi, Claudio</a> (1997). <a rel="nofollow" class="external text" href="https://www.ams.org/journals/bull/1997-34-01/S0273-0979-97-00689-7/S0273-0979-97-00689-7.pdf">"Review: <i>Conjugacy classes in semisimple algebraic groups</i>, by James E. Humphreys"</a> <span class="cs1-format">(PDF)</span>. <i><a href="/wiki/Bulletin_of_the_American_Mathematical_Society" title="Bulletin of the American Mathematical Society">Bulletin of the American Mathematical Society</a></i>. <b>34</b> (1): 55–56. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0273-0979-97-00689-7">10.1090/s0273-0979-97-00689-7</a></span>. <a href="/wiki/MR_(identifier)" class="mw-redirect" title="MR (identifier)">MR</a> <a rel="nofollow" class="external text" href="https://mathscinet.ams.org/mathscinet-getitem?mr=1343976">1343976</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+of+the+American+Mathematical+Society&rft.atitle=Review%3A+Conjugacy+classes+in+semisimple+algebraic+groups%2C+by+James+E.+Humphreys&rft.volume=34&rft.issue=1&rft.pages=55-56&rft.date=1997&rft_id=info%3Adoi%2F10.1090%2Fs0273-0979-97-00689-7&rft_id=https%3A%2F%2Fmathscinet.ams.org%2Fmathscinet-getitem%3Fmr%3D1343976%23id-name%3DMR&rft.aulast=Procesi&rft.aufirst=Claudio&rft_id=https%3A%2F%2Fwww.ams.org%2Fjournals%2Fbull%2F1997-34-01%2FS0273-0979-97-00689-7%2FS0273-0979-97-00689-7.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJames+E.+Humphreys" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBenson2007" class="citation journal cs1">Benson, Dave (2007). "Review: <i>Modular representations of finite groups of Lie type</i>, by James E. Humphreys". <i>SIAM Review</i>. <b>49</b> (1): 129–131. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1137%2FSIREAD000049000001000123000001">10.1137/SIREAD000049000001000123000001</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a> <a rel="nofollow" class="external text" href="https://www.jstor.org/stable/20453917">20453917</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=SIAM+Review&rft.atitle=Review%3A+Modular+representations+of+finite+groups+of+Lie+type%2C+by+James+E.+Humphreys&rft.volume=49&rft.issue=1&rft.pages=129-131&rft.date=2007&rft_id=info%3Adoi%2F10.1137%2FSIREAD000049000001000123000001&rft_id=https%3A%2F%2Fwww.jstor.org%2Fstable%2F20453917%23id-name%3DJSTOR&rft.aulast=Benson&rft.aufirst=Dave&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJames+E.+Humphreys" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSoergel,_Wolfgang2010" class="citation journal cs1"><a href="/wiki/Wolfgang_Soergel" title="Wolfgang Soergel">Soergel, Wolfgang</a> (2010). <a rel="nofollow" class="external text" href="https://www.ams.org/journals/bull/2010-47-02/S0273-0979-09-01266-X/">"Review: <i>Representations of semisimple Lie algebras in the BGG category <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathcal {O}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-tex-caligraphic" mathvariant="script">O</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathcal {O}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6ae2ed4058fb748a183d9ada8aea50a00d0c89f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.85ex; height:2.176ex;" alt="{\displaystyle {\mathcal {O}}}"></span></i>, by James E. Humphreys"</a>. <i>Bull. Amer. Math. Soc. (N.S.)</i>. <b>47</b> (2): 367–371. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1090%2Fs0273-0979-09-01266-X">10.1090/s0273-0979-09-01266-X</a></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bull.+Amer.+Math.+Soc.+%28N.S.%29&rft.atitle=Review%3A+Representations+of+semisimple+Lie+algebras+in+the+BGG+category+MATH+RENDER+ERROR%2C+by+James+E.+Humphreys&rft.volume=47&rft.issue=2&rft.pages=367-371&rft.date=2010&rft_id=info%3Adoi%2F10.1090%2Fs0273-0979-09-01266-X&rft.au=Soergel%2C+Wolfgang&rft_id=https%3A%2F%2Fwww.ams.org%2Fjournals%2Fbull%2F2010-47-02%2FS0273-0979-09-01266-X%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJames+E.+Humphreys" class="Z3988"></span></span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.maa.org/programs/maa-awards/writing-awards/representations-of-sl-2p">"Representations of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \operatorname {SL} (2,p)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>SL</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mi>p</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \operatorname {SL} (2,p)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bd7e15cc7e6aac551139d2a57983db07a92b544" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.92ex; height:2.843ex;" alt="{\displaystyle \operatorname {SL} (2,p)}"></span>"</a>. <i>maa.org</i>. <a href="/wiki/Mathematical_Association_of_America" title="Mathematical Association of America">Mathematical Association of America</a><span class="reference-accessdate">. Retrieved <span class="nowrap">January 28,</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=maa.org&rft.atitle=Representations+of+MATH+RENDER+ERROR&rft_id=http%3A%2F%2Fwww.maa.org%2Fprograms%2Fmaa-awards%2Fwriting-awards%2Frepresentations-of-sl-2p&rfr_id=info%3Asid%2Fen.wikipedia.org%3AJames+E.+Humphreys" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=James_E._Humphreys&action=edit&section=6" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.math.umass.edu/~jeh/">Homepage</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output 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