Matching theorems for twisted orbital integrals
type: Item
instance of: scholarly article
title: Matching theorems for twisted orbital integrals
zbMATH Open document ID: 0853.22007
published in: Pacific Journal of Mathematics
publication date: 1996-11-07T00:00:00Z
review text: Let \(F\) be a \(p\)-adic field and \(E\) a cyclic extension of \(F\) of degree \(d\) corresponding to the character \(\kappa\) of \(F^\times\). For any positive integer \(m\), we can consider \(H = GL (m,E)\) as a subgroup of \(G = GL (md,F)\). In this paper we discuss matching of orbital integrals between \(H\) and \(G\). Specifically, ordinary orbital integrals corresponding to regular semisimple elements of \(H\) are matched with orbital integrals on \(G\) which are twisted by the character \(\kappa\). For the general situation we only match functions which are smooth and compactly supported on the regular set. If the extension \(E/F\) is unramified, we are able to match arbitrary smooth, compactly supported functions.
Mathematics Subject Classification ID: 22E35
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 912152
zbMATH Keywords: \(p\)-adic field
zbMATH Keywords: matching of orbital integrals
zbMATH Keywords: orbital integrals
author: Rebecca A. Herb
MaRDI profile type: Publication
full work available at URL: pjm.1995.171.409
OpenAlex ID: W1581738488
DOI: 10.2140/PJM.1995.171.409
description: scientific article; zbMATH DE number 912152