On elliptic tempered characters
type: Item
instance of: scholarly article
title: On elliptic tempered characters
zbMATH Open document ID: 0822.22011
DOI: 10.1007/BF02392767
author: James Arthur
published in: Acta Mathematica
publication date: 1995-10-08T00:00:00Z
review text: Let \(G\) be a connected reductive algebraic group over a local field of characteristic zero (either real or \(p\)-adic). This paper considers the characters of elliptic tempered representations of \(G\). The author defines a family of virtual tempered characters, (each the trace of an induced representation twisted by an intertwining operator). Part of the local trace formula can be expanded in terms of these virtual characters, and this leads to an expression of the (noninvariant) trace formula as a local trace formula whose terms are all invariant. If \(f\) is a cuspidal function, \(\gamma\) a \(G\)-regular element in the elliptic set of a Levi subgroup \(M\), then the author shows how to expand the orbital integral \(I_ M(\gamma, f)\) in terms of the elliptic tempered virtual characters. There is a parallel expansion for some related distributions in terms of truncated virtual characters. These results are then used to establish orthogonality relations for the virtual tempered characters and also a local proof of Kazhdan's Theorem that invariant orbital integrals are supported on characters. There are also applications to certain contour integrals and residues.
Mathematics Subject Classification ID: 22E50
Mathematics Subject Classification ID: 11F72
Mathematics Subject Classification ID: 22E35
zbMATH DE Number: 508630
zbMATH Keywords: connected reductive algebraic groups
zbMATH Keywords: characters of elliptic tempered representations
zbMATH Keywords: virtual tempered characters
zbMATH Keywords: local trace formula
zbMATH Keywords: orbital integrals
zbMATH Keywords: orthogonality relations
zbMATH Keywords: invariant orbital integrals
Wikidata QID: Q97994343
reviewed by: Joe Repka
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02392767
OpenAlex ID: W2031284695
description: scientific article; zbMATH DE number 508630