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To link to an nLab page but show a different link text, do the following: [[ name of page | link text to show ]].</li> <li style="font-size: 0.8em">LaTeX can be used inside single dollar signs (inline) or double dollar signs or \[ and \], as usual. </li> <li style="font-size: 0.8em">To create a table of contents, add \tableofcontents on its own line.</li> <li style="font-size: 0.8em">For a theorem or proof, use \begin{theorem} \end{theorem} as you would in LaTeX. Labelling and referencing is exactly as in LaTeX, with use of \label and \ref. The full list of supported environments can be found in the <a href="/nlab/show/HowTo#DefinitionTheoremProofEnvironments">HowTo</a>. </li> <li style="font-size: 0.8em">Tikz can be used for figures almost exactly as in LaTeX. Similarly, tikz-cd and xymatrix can be used for commutative diagrams. See the <a href="/nlab/show/HowTo#diagrams">HowTo</a>.</li> <li style="font-size: 0.8em">As an alternative to the Markdown syntax for sections (headings), one can use the usual LaTeX syntax \section, \subsection, etc.</li> <li style="font-size: 0.8em">For further help, see the <a href="/nlab/show/HowTo">HowTo</a>, or you are very welcome to ask at the <a href="https://nforum.ncatlab.org/">nForum</a>.</li> </ol> </div> <form accept-charset="utf-8" action="/nlab/save/representation+theory+-+contents" id="editForm" method="post"> <div style="display: none;"> <input name="see_if_human" id="see_if_human" style="tabindex: -1; autocomplete: off"/> </div> <div> <textarea name="content" id="content" style="height: 45em; width: 70%;">**[[representation theory]]** **[[geometric representation theory]]** ## Ingredients * [[linear algebra]], [[algebra]], [[higher algebra]] ## Definitions {#sidebar_definitions} [[representation]], [[2-representation]], [[∞-representation]] * [[group]], [[∞-group]] * [[group algebra]], [[algebraic group]], [[Lie algebra]] * [[vector space]], [[n-vector space]] * [[affine space]], [[symplectic vector space]] * [[action]], [[∞-action]] * [[module]], [[equivariant object]] * [[bimodule]], [[Morita equivalence]] * [[induced representation]], [[Frobenius reciprocity]] * [[Hilbert space]], [[Banach space]], [[Fourier transform]], [[functional analysis]] * [[orbit]], [[coadjoint orbit]], [[Killing form]] * [[unitary representation]] * [[geometric quantization]], [[coherent state]] * [[socle]], [[quiver]] * [[module algebra]], [[comodule algebra]], [[Hopf action]], [[measuring]] ## Geometric representation theory * [[D-module]], [[perverse sheaf]], * [[Grothendieck group]], [[lambda-ring]], [[symmetric function]], [[formal group]] * [[principal bundle]], [[torsor]], [[vector bundle]], [[Atiyah Lie algebroid]] * [[geometric function theory]], [[groupoidification]] * [[Eilenberg-Moore category]], [[algebra over an operad]], [[actegory]], [[crossed module]] * [[reconstruction theorems]] ## Theorems {#sidebar_theorems} * [[Borel-Weil-Bott theorem]] * [[Be?linson-Bernstein localization]] * [[Kazhdan-Lusztig theory]] * [[BBDG decomposition theorem]] <div markdown="1">[Edit this sidebar](/nlab/edit/representation+theory+-+contents)</div></textarea> <p> <input id="alter_title" name="alter_title" onchange="toggleVisibility();" type="checkbox" value="1" /> <label for="alter_title">Change page name.</label><br/> <span id="title_change" style="display:none"><label for="new_name">New name:</label> <input id="new_name" name="new_name" onblur="addRedirect();" type="text" value="representation theory - contents" /></span> </p> <div> <p style="font-size: 0.8em; width: 70%;"> For non-trivial edits, please briefly describe your changes below. 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