On finite group actions on reductive groups and buildings
type: Item
instance of: scholarly article
title: On finite group actions on reductive groups and buildings
zbMATH Open document ID: 1020.22003
author: Gopal Prasad
author: Jiu-Kang Yu
published in: Inventiones Mathematicae
publication date: 2002-08-08T00:00:00Z
full work available at URL: http://hdl.handle.net/2027.42/42022
review text: Let \(H\) be a connected reductive group over a non-Archimedean local field \(k\), and let \(F\subset \text{Aut}_k(H)\) be a finite group of order \(f\) not divisible by the residual characteristic of \(k\). Let \(G\) be the identity component of the subgroup of \(H\) consisting of points fixed by \(F\). The authors prove that \(G\) is reductive (this is actually proved for any field \(k\), provided \(\operatorname {char} k\) does not divide \(f\)), and that the Bruhat-Tits building \(\mathcal B(G)\) of \(G\) can be identified with the set of \(F\)-fixed points of \(\mathcal B(H)\). The last result was recently proved by several authors for a number of special cases. A similar problem for spherical buildings is also considered.
Mathematics Subject Classification ID: 22E20
Mathematics Subject Classification ID: 20E42
zbMATH DE Number: 1777232
zbMATH Keywords: reductive group
zbMATH Keywords: building
zbMATH Keywords: spherical building
zbMATH Keywords: automorphism
reviewed by: Anatoly N. Kochubei
MaRDI profile type: Publication
OpenAlex ID: W2101738989
DOI: 10.1007/S002220100182
description: scientific article; zbMATH DE number 1777232