On the classification of irreducible representations of affine Hecke algebras with unequal parameters

DOI10.1090/S1088-4165-2012-00406-XzbMath1272.20003arXiv1008.0177MaRDI QIDQ2889344

Maarten Solleveld

Publication date: 7 June 2012

Published in: Representation Theory of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1008.0177

zbMATH Keywords

irreducible representationsfinite Weyl groupsaffine Hecke algebrasSpringer correspondencereductive \(p\)-adic groupsaffine reflections

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Representations of Lie and linear algebraic groups over local fields (22E50) Linear algebraic groups over local fields and their integers (20G25)

Related Items

A uniform classification of discrete series representations of affine Hecke algebras ⋮ Extensions of tempered representations ⋮ ON FORMAL DEGREES OF UNIPOTENT REPRESENTATIONS ⋮ Endomorphism algebras and Hecke algebras for reductive \(p\)-adic groups ⋮ Classifying right-angled Hecke \(\mathrm{C}^\ast\)-algebras via \(K\)-theoretic invariants ⋮ The degenerate principal series representations of exceptional groups of type \(E_7\) over \(p\)-adic fields ⋮ The cocenter of the graded affine Hecke algebra and the density theorem ⋮ Hochschild homology of twisted crossed products and twisted graded Hecke algebras ⋮ A local Langlands correspondence for unipotent representations ⋮ Hochschild homology of affine Hecke algebras. ⋮ Some aspects of the geometric structure of the smooth dual of $p$-adic reductive groups ⋮ Geometric structure in smooth dual and local Langlands conjecture ⋮ Conjectures about 𝑝-adic groups and their noncommutative geometry ⋮ Proof of the Aubert-Baum-Plymen-Solleveld conjecture for split classical groups ⋮ The Mackey bijection for complex reductive groups and continuous fields of reduced group C*-algebras ⋮ Affine Hecke algebras and their representations ⋮ Algebraic and analytic Dirac induction for graded affine Hecke algebras ⋮ Topological K-theory of affine Hecke algebras ⋮ Regular Bernstein blocks ⋮ The periodic cyclic homology of crossed products of finite type algebras ⋮ Geometric structure for the principal series of a split reductive \(p\)-adic group with connected centre ⋮ Langlands parameters, functoriality and Hecke algebras

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