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{{Short description|Group representation via algebra automorphisms}} {{distinguish|algebra representation}} ...

...' is an [[associative algebra]] related to the [[partial representation]]s of a [[group (mathematics)|group]]. * [[Group representation]] ...

...<math>(\mathfrak{g},K)</math>-module, then its Harish-Chandra module is a representation with desirable factorization properties. ...dra module'' of <math>\pi</math> is the subspace ''X'' of ''V'' consisting of the [[K-finite]] smooth vectors in ''V''. This means that ''X'' includes ex ...

...fand, D. Raikov, "Irreducible unitary representations of locally bicompact groups", Recueil Mathématique. N.S., 13(55):2–3 (1943), 301–316)</ref> ...Hisaaki. "Unitary representations of locally compact groups. Reproduction of Gelfand–Raikov's theorem." Osaka Mathematical Journal 1.1 (1949): 81–89].</ ...

...ion|representation]] of a [[group (mathematics)|group]] or a [[Lie algebra representation|Lie algebra]] on a [[symplectic vector space]] (''V'', ''ω'') which preserv ...'''F''' is the [[field (mathematics)|field]] of scalars. A representation of a group ''G'' preserves ''ω'' if ...

...H'' of a [[finite group]] ''G''. It is a special case of a [[Hecke algebra of a locally compact group]]. ...]] zero, ''G'' a finite [[group (mathematics)|group]] and ''H'' a subgroup of ''G''. Let <math>F[G]</math> denote the ...

...group of [[permutation matrices]]. The term also refers to the combination of the two. ==Abstract permutation representation== ...

...ion|Linear representation of a group on the tangent space to a fixed point of the group.}} ..., the '''isotropy representation''' is a natural [[linear representation]] of a [[Lie group]], that is [[Lie group action|acting]] on a manifold, on the ...

...duction of a class function|induction]] <math>\operatorname{Ind}(f)</math> of a [[class function]] ''f'' on ''H'' given by the formula ...nd}(f)</math> calculates the character of the induced representation ''V'' of ''G''.<ref>{{citation ...

{{Short description|Conjecture in modular representation theory}} ...t1=Brauer |first1=Richard D. |year=1963 |chapter=Representations of finite groups |title=Lectures in Mathematics |volume=1 |publisher=Wiley | pages=133–175 | ...

...l Ludwig Siegel|editor-surname1= Annals of Mathematics|title=Discontinuous groups|volume=44|issue=4|at=pp.&nbsp;674−689|date=1943 [[Category:Topological groups]] ...

In mathematical [[representation theory]], the '''Harish-Chandra transform''' is a linear map from functions on a [ The Harish-Chandra transform ''f''^''P'' of a function ''f'' on the group ''G'' is given by ...

...lass]] <math>\lambda_V</math> of a complex [[Representation of a Lie group|representation]] <math>V</math>. The term "cannibalistic" for these classes was introduced *{{citation|first=J. Frank |last=Adams|authorlink=Frank Adams| title=On the groups <math>J(X)</math>. II.|journal=[[Topology (journal)|Topology]] |volume=3|ye ...

...(discrete subgroup)|lattices]] in Lie groups, often under the name ''field of definition''. == Fuchsian and Kleinian groups == ...

...the [[representation theory]] of [[algebraic group]]s. She is a professor of mathematics at the [[École Polytechnique Fédérale de Lausanne]] in Switzerl ...egon]] in 1985. Her dissertation, ''Certain Embeddings of Simple Algebraic Groups'', was supervised by [[Gary Seitz]].{{r|mg}} As a faculty member at [[Wesle ...

...nnected compact complex Lie group is a [[complex torus]]; i.e., a quotient of <math>\mathbb{\Complex}^n</math> by a lattice. *{{Cite book| title = Representation theory of semisimple groups. An overview based on examples ...

...of ''G'' and ''K'' is a [[maximal compact subgroup]] of ''G''.<ref>Page 12 of {{harvnb|Doran|Varadarajan|2000}}</ref> ...sentation]] of ''K'' (without regard to the [[topological space|topology]] of ''K'') satisfying the following three conditions ...

...andra|1976a}}; {{harvtxt|Harish-Chandra|1976b}}</ref> Trombi gave a survey of Harish-Chandra's work on this.<ref>{{harvtxt|Trombi|1989}}</ref> *''x'' is an element of a semisimple group ''G'' ...

{{Short description|Formula in representation theory}} ...imple complex [[Lie algebra]] in a [[tensor product]] of two [[irreducible representation]]s. ...

In [[mathematics]], specifically in the field of [[modular representation theory]], the | title = Proceedings of the international symposium on algebraic number theory, Tokyo and Nikko, 1955 ...