On the Hecke algebra of a type for unramified \(p\)-adic unitary groups
type: Item
instance of: scholarly article
title: On the Hecke algebra of a type for unramified \(p\)-adic unitary groups
zbMATH Open document ID: 1196.22012
author: Kazutoshi Kariyama
published in: Journal of Algebra
publication date: 2010-06-08T00:00:00Z
review text: Let \(F\) be a non-Archimedean local field with odd residue characteristic that is equipped with a Galois involution with fixed field \(F_o\). Let \(G\) be either the symplectic group \(Sp_{2N}(F)\) over \(F\) or an unramified unitary group over \(F_o\). The key result of this paper is the following Theorem: If a pair (\(J_P, \lambda_P)\) in the unramified group \(G\) that consists of a Levi subgroup \(M\) of \(G\) and of an irreducible supercuspidal representation \(\pi\) of \(M\) is of simple type, then the Hecke algebra \(H(G, \lambda_P)\) is generic.
Mathematics Subject Classification ID: 22E50
Mathematics Subject Classification ID: 22D99
zbMATH DE Number: 5718174
zbMATH Keywords: unramified \(p\)-adic unitary group
zbMATH Keywords: non-archimedean local field
zbMATH Keywords: Galois involution
zbMATH Keywords: symplectic group
zbMATH Keywords: Bernstein block
zbMATH Keywords: inertial classes of pairs
zbMATH Keywords: simple-type pair
zbMATH Keywords: Levi factor
zbMATH Keywords: parabolic group
zbMATH Keywords: Hecke algebra
zbMATH Keywords: Weyl group
zbMATH Keywords: generic Hecke algebra
zbMATH Keywords: irreducible supercuspidal representation
reviewed by: Eugene Kryachko
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2010.03.002
OpenAlex ID: W1975430349
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DOI: 10.1016/J.JALGEBRA.2010.03.002
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description: scientific article; zbMATH DE number 5718174