The Schwartz algebra of an affine Hecke algebra

DOI10.1515/CRELLE.2008.090zbMath1173.22014arXivmath/0312517OpenAlexW1964098597MaRDI QIDQ3600017

Patrick Delorme, Eric M. Opdam

Publication date: 10 February 2009

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0312517

zbMATH Keywords

Fourier transformWeyl groupsmatrix coefficientsHilbert algebraaffine Hecke algebraSchwartz algebrareductive \(p\)-adic groups

Mathematics Subject Classification ID

Analysis on (p)-adic Lie groups (22E35) Representations of Lie and linear algebraic groups over local fields (22E50)

Related Items

A uniform classification of discrete series representations of affine Hecke algebras ⋮ On the classification of irreducible representations of affine Hecke algebras with unequal parameters ⋮ Extensions of tempered representations ⋮ Smooth duals of inner forms of \(\mathrm{GL}_n\) and \(\mathrm{SL}_n\) ⋮ Tempered modules in exotic Deligne-Langlands correspondence ⋮ Spectral correspondences for affine Hecke algebras ⋮ Hochschild homology of twisted crossed products and twisted graded Hecke algebras ⋮ Discrete series characters for affine Hecke algebras and their formal degrees. ⋮ A local Langlands correspondence for unipotent representations ⋮ Hecke algebras with parameters and representations of a classical \(p\)-adic group: preservation of tempered spectrum ⋮ Hochschild homology of affine Hecke algebras. ⋮ Parabolically induced representations of graded Hecke algebras. ⋮ On calibrated representations and the Plancherel theorem for affine Hecke algebras ⋮ Affine Hecke algebras and their representations ⋮ Generalized Springer correspondence and Green functions for type \(B/C\) graded Hecke algebras. ⋮ Topological K-theory of affine Hecke algebras ⋮ Homological algebra for affine Hecke algebras.

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