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- Hecke_algebra_of_a_locally_compact_group abstract "In mathematics, a Hecke algebra of a locally compact group is an algebra of bi-invariant measures under convolution. Let (G,K) be a pair consisting of a unimodular locally compact topological group G and a closed subgroup K of G. Then the space of bi-K-invariant continuous functions of compact supportC[K\G/K] can be endowed with a structure of an associative algebra under the operation of convolution. This algebra is denoted H(G//K) and called the Hecke ring of the pair (G,K). If we start with a Gelfand pair then the resulting algebra turns out to be commutative. In particular, this holds when G = SLn(Qp) and K = SLn(Zp) and the representations of the corresponding commutative Hecke ring were studied by Ian G. Macdonald. On the other hand, in the case G = SL2(Q) and K = SL2(Z) we arrive at the abstract ring behind Hecke operators in the theory of modular forms, which gave the name to Hecke algebras in general. The case leading to the Hecke algebra of a finite Weyl group is when G is the finite Chevalley group over a finite field with pk elements, and B is its Borel subgroup. Iwahori showed that the Hecke ring H(G//B) is obtained from the generic Hecke algebra Hq of the Weyl group W of G by specializing the indeterminate q of the latter algebra to pk, the cardinality of the finite field. George Lusztig remarked in 1984 (Characters of reductive groups over a finite field, xi, footnote):I think it would be most appropriate to call it the Iwahori algebra, but the name Hecke ring (or algebra) given by Iwahori himself has been in use for almost 20 years and it is probably too late to change it now.Iwahori and Matsumoto (1965) considered the case when G is a group of points of a reductive algebraic group over a non-archimedean local field K, such as Qp, and K is what is now called an Iwahori subgroup of G. The resulting Hecke ring is isomorphic to the Hecke algebra of the affine Weyl group of G, or the affine Hecke algebra, where the indeterminate q has been specialized to the cardinality of the residue field of K.".
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- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Affine_Hecke_algebra.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Affine_Weyl_group.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Borel_subgroup.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Category:Representation_theory.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Chevalley_group.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Compact_support.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Continuous_function.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Convolution.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Coxeter_group.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Finite_field.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Gelfand_pair.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink George_Lusztig.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Group_(mathematics).
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Group_of_Lie_type.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Haar_measure.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Hecke_operator.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Hecke_operators.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Ian_G._Macdonald.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Iwahori_subgroup.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Local_field.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Locally_compact.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Locally_compact_group.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Locally_compact_space.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Locally_compact_topological_group.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Modular_form.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Modular_forms.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Reductive_algebraic_group.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Reductive_group.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Residue_field.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Support_(mathematics).
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Unimodular_group.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLink Weyl_group.
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLinkText "Hecke algebra of a locally compact group".
- Hecke_algebra_of_a_locally_compact_group wikiPageWikiLinkText "Hecke algebra".
- Hecke_algebra_of_a_locally_compact_group hasPhotoCollection Hecke_algebra_of_a_locally_compact_group.
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- Hecke_algebra_of_a_locally_compact_group subject Category:Representation_theory.
- Hecke_algebra_of_a_locally_compact_group hypernym Algebra.
- Hecke_algebra_of_a_locally_compact_group type Article.
- Hecke_algebra_of_a_locally_compact_group type Article.
- Hecke_algebra_of_a_locally_compact_group type Field.
- Hecke_algebra_of_a_locally_compact_group comment "In mathematics, a Hecke algebra of a locally compact group is an algebra of bi-invariant measures under convolution. Let (G,K) be a pair consisting of a unimodular locally compact topological group G and a closed subgroup K of G. Then the space of bi-K-invariant continuous functions of compact supportC[K\G/K] can be endowed with a structure of an associative algebra under the operation of convolution. This algebra is denoted H(G//K) and called the Hecke ring of the pair (G,K).".
- Hecke_algebra_of_a_locally_compact_group label "Hecke algebra of a locally compact group".
- Hecke_algebra_of_a_locally_compact_group sameAs m.0gxzzl9.
- Hecke_algebra_of_a_locally_compact_group sameAs Q17097986.
- Hecke_algebra_of_a_locally_compact_group sameAs Q17097986.
- Hecke_algebra_of_a_locally_compact_group wasDerivedFrom Hecke_algebra_of_a_locally_compact_group?oldid=584662685.
- Hecke_algebra_of_a_locally_compact_group isPrimaryTopicOf Hecke_algebra_of_a_locally_compact_group.