Hecke algebra isomorphisms for GL(n) over a p-adic field
type: Item
instance of: scholarly article
title: Hecke algebra isomorphisms for GL(n) over a p-adic field
zbMATH Open document ID: 0715.22019
DOI: 10.1016/0021-8693(90)90182-N
author: Allen Moy
author: Roger Howe
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: The results on the existence and uniqueness of minimal K-types for irreducible admissible representations of \(G=GL(n,F)\) (F a p-adic field) that have recently been obtained by the same authors [Astérisque 171- 172, 257-273 (1989; see the preceding review Zbl 0715.22018)] are refined and then used to obtain further progress towards the classification of the irreducible admissible representations of G. In particular for the tame case it is shown that to each irreducible admissible representation \(\pi\) of G that is square integrable modulo the center of G one can associate a parahoric subgroup K with a representation \(\theta\) of K containing a minimal K-type of \(\pi\), an extension E of F and a subgroup \(G'=GL(m,E)\subset G\) with \(m(E:F)=n\) such that \(K\cap G'=B'\) is an Iwahori subgroup of \(G'\) and such that one has a Hecke algebra isomorphism preserving supports between \(H(G'//B',1)\) and H(G//K,\(\theta\)). Furthermore the pair (K,\(\theta\)) has multiplicity one in \(\pi\) in analogy with the minimal K-types in the real case.
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 4177416
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: minimal K-types
zbMATH Keywords: p-adic field
zbMATH Keywords: irreducible admissible representations
zbMATH Keywords: square integrable
zbMATH Keywords: parahoric subgroup
zbMATH Keywords: Iwahori subgroup
zbMATH Keywords: Hecke algebra isomorphism
reviewed by: Rainer Schulze-Pillot
MaRDI profile type: Publication
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full work available at URL: 0021-8693(90)90182-n
OpenAlex ID: W2095462693
description: scientific article; zbMATH DE number 4177416