On geometric transfer in real twisted endoscopy
type: Item
instance of: scholarly article
title: On geometric transfer in real twisted endoscopy
zbMATH Open document ID: 1259.22007
author: D. Shelstad
published in: Annals of Mathematics. Second Series
publication date: 2013-01-03T00:00:00Z
review text: Consider a connected reductive algebraic group \(G\) over \(\mathbb R\) with an automorphism \(\theta\) defined over \(\mathbb R\) and a character \(\omega\) of \(G({\mathbb R})\). The geometric transfer proved in this article is an equality between weighted sums of \((\theta, \omega)\)-twisted orbital integrals on \(G({\mathbb R})\) and stable orbital integrals on an endoscopic group for \((G,\theta,\omega)\). Essential for the proof is the study of the behaviour of stable orbital integrals (resp., of weighted sums of twisted orbital integrals) around a semisimple element with centralizer of type \(A_1\). The author makes use of the fact that the relative transfer factor, i.e., the quotient of two values of the transfer factor, is canonical (see [\textit{R. E. Kottwitz} and \textit{D. Shelstad}, Foundations of twisted endoscopy. Astérisque. 255. Paris: Société Mathématique de France (1999; Zbl 0958.22013)]). This simplifies the argument and gives at the same time a shorter proof for the known case of non-twisted endoscopy.
Mathematics Subject Classification ID: 22E45
Mathematics Subject Classification ID: 22E99
zbMATH DE Number: 6121653
zbMATH Keywords: endoscopic transfer
zbMATH Keywords: real Lie groups
zbMATH Keywords: orbital integrals
reviewed by: J. G. M. Mars
MaRDI profile type: Publication
full work available at URL: annals.2012.176.3.9
OpenAlex ID: W2120093398
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DOI: 10.4007/ANNALS.2012.176.3.9
description: scientific article; zbMATH DE number 6121653