Limit cones of discrete subgroups of reductive groups over a local field
type: Item
instance of: scholarly article
title: Limit cones of discrete subgroups of reductive groups over a local field
zbMATH Open document ID: 1018.22004
author: Jean-François Quint
published in: Transformation Groups
publication date: 2003-09-02T00:00:00Z
review text: For a given reductive \(K\)-group \(G= {\mathbf G}(K)\) over a local field \(K\), define \(\Gamma\) as a subgroup of \(G\) and its limit cone as the closed cone generated by the set elements in a Weyl chamber of \(G\) conjugate to the hyperbolic components of \(\Gamma\) [\textit{Y. Benoist}, Geom. Funct. Anal. 7, 1-47 (1997; Zbl 0947.22003)]. If \(K\) is non-Archimedean, it is proved that each closed convex cone with a rational support and stable relative to the opposition involution of a vector Weyl chamber of \(G\) is the limit cone of some Zariski dense subgroup of \(G\).
Mathematics Subject Classification ID: 22E15
Mathematics Subject Classification ID: 20G25
zbMATH DE Number: 1885651
zbMATH Keywords: reductive \(K\)-group
zbMATH Keywords: limit cone
zbMATH Keywords: Weyl chamber
zbMATH Keywords: Zariski dense subgroup
reviewed by: Eugene Kryachko
MaRDI profile type: Publication
full work available at URL: s00031-002-0013-2
OpenAlex ID: W2042504950
DOI: 10.1007/S00031-002-0013-2
description: scientific article; zbMATH DE number 1885651