The characters of supercuspidal representations as weighted orbital integrals
type: Item
instance of: scholarly article
title: The characters of supercuspidal representations as weighted orbital integrals
zbMATH Open document ID: 0652.22009
DOI: 10.1007/BF02837809
author: James Arthur
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1987-01-01T00:00:00Z
review text: The author shows how the character of a supercuspidal representation of a reductive Lie group over a non-archimedean local field of characteristic zero is given, up to a factor, as an orbital integral of a matrix coefficient of the representation. The orbital integral is of the type that arise in the author's general version of the Selberg trace formula. The proof is an ingenious deduction using the geometry of reductive groups from an expression of Harish-Chandra's giving the character in terms of an integral of a matrix coefficient.
Mathematics Subject Classification ID: 22E35
Mathematics Subject Classification ID: 11F33
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 4063418
zbMATH Keywords: character
zbMATH Keywords: supercuspidal representation
zbMATH Keywords: reductive Lie group
zbMATH Keywords: non- archimedean local field
zbMATH Keywords: orbital integral
zbMATH Keywords: Selberg trace formula
reviewed by: Samuel James Patterson
MaRDI profile type: Publication
cites work: The characters of discrete series as orbital integrals
cites work: A trace formula for reductive groups. I: Terms associated to classes in G(Q)
cites work: The trace formula in invariant form
cites work: On a Family of Distributions Obtained from Eisenstein Series II: Explicit Formulas
cites work: Harmonic analysis on reductive \(p\)-adic groups. Notes by G. van Dijk
full work available at URL: https://doi.org/10.1007/bf02837809
OpenAlex ID: W1985355182
description: scientific article; zbMATH DE number 4063418