Residual spectrum of split reductive groups supported in a Borel subgroup under isogenies
type: Item
instance of: scholarly article
title: Residual spectrum of split reductive groups supported in a Borel subgroup under isogenies
zbMATH Open document ID: 1279.22027
author: Henry H. Kim
author: Wook-Dong Kim
published in: Manuscripta Mathematica
publication date: 2013-05-17T00:00:00Z
review text: Let \(G\) and \(G'\) be almost simple semi-simple split groups. For a central isogeny \(G\) to \(G'\), the authors describe a relationship between the residual spectrum of \(G\) and \(G'\). In this paper, the authors study the residual spectrum of cuspidal support (\(B, \chi\)) and (\(B', \chi'\)), where \(B\) and \(B'\) are Borel subgroups of \(G\) and \(G'\) respectively, and \(\chi\) and \(\chi'\) are unitary characters on the tori contained in \(B\) and \(B'\). If the residual spectrum of a group in a given isogeny class is known, then all residual spectrums of groups in this isogeny class can be obtained by the relationship described by the authors. As indicated in this paper, one can obtain the residual spectrum of Spin\((2n+1)\) by the residual spectrum of SO\((2n+1)\) which is studied in [\textit{H. Kim}, Pac. J. Math. 199, No. 2, 417--455 (2001; Zbl 1047.22016)]. In addition, the authors give Arthur parameters of those residual spectrums.
reviewed by: Lei Zhang
Mathematics Subject Classification ID: 22E55
Mathematics Subject Classification ID: 11F70
zbMATH DE Number: 6164101
MaRDI profile type: Publication
full work available at URL: s00229-012-0557-y
OpenAlex ID: W2022206107
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DOI: 10.1007/S00229-012-0557-Y
description: scientific article; zbMATH DE number 6164101