Local character expansions and Shalika germs for GL(n)
type: Item
instance of: scholarly article
title: Local character expansions and Shalika germs for GL(n)
zbMATH Open document ID: 0841.22008
DOI: 10.1007/BF01446300
author: Fiona Murnaghan
published in: Mathematische Annalen
publication date: 1996-03-31T00:00:00Z
full work available at URL: https://eudml.org/doc/165410
review text: We study the values of characters of irreducible supercuspidal representations of \(p\)-adic general linear groups. Under the assumption that the residual characteristic of the field is greater than the rank of the group, we prove that on some neighbourhood of the identity element the character of such a representation coincides with a positive multiple of the Fourier transform of a regular elliptic adjoint orbit (composed with the inverse of the exponential map). As a consequence, the coefficients of the Fourier transforms of nilpotent adjoint orbits in Harish-Chandra's local character expansion are shown to be positive multiples of the Shalika germs evaluated at the elliptic orbit.
Mathematics Subject Classification ID: 22E35
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 861919
zbMATH Keywords: \(p\)-adic general linear groups
zbMATH Keywords: characters
zbMATH Keywords: irreducible supercuspidal representations
zbMATH Keywords: Fourier transform
zbMATH Keywords: regular elliptic adjoint orbit
zbMATH Keywords: Fourier transforms
zbMATH Keywords: nilpotent adjoint orbits
zbMATH Keywords: Harish-Chandra's local character expansion
zbMATH Keywords: Shalika germs
zbMATH Keywords: elliptic orbit
MaRDI profile type: Publication
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OpenAlex ID: W2013292720
description: scientific article; zbMATH DE number 861919