Compactifications of symmetric and locally symmetric spaces
type: Item
instance of: scholarly article
title: Compactifications of symmetric and locally symmetric spaces
zbMATH Open document ID: 1027.22011
author: Lizhen Ji
author: Armand Borel
published in: Mathematical Research Letters
publication date: 2003-09-08T00:00:00Z
review text: Let \(G\) be a connected non-compact linear real semisimple Lie group, \(K\) a maximal compact subgroup of \(G\), and \(\Gamma\) an arithmetically defined not co-compact subgroup of \(G\). The authors define several known compactifications of \(G\): \(X=G/K\), \(\Gamma\backslash G\) and \(\Gamma\backslash X\), Satake compactifications of \(X=G/K\) and the DeConcini-Procesi compactification of \(G_c/K_c\), and the Martin compactifications of \(X\), Satake, and Borel-Serre compactifications of \(\Gamma\backslash X\) by the attachment method. The main purpose of this note is to announce a uniform construction of most known compactifications.
Mathematics Subject Classification ID: 22E15
Mathematics Subject Classification ID: 22E46
zbMATH DE Number: 1930993
zbMATH Keywords: symmetric space
zbMATH Keywords: locally symmetric space
zbMATH Keywords: linear real semisimple Lie group
zbMATH Keywords: Satake compactifications
zbMATH Keywords: DeConcini-Procesi compactification
zbMATH Keywords: Martin compactifications
reviewed by: Bang-Yen Chen
MaRDI profile type: Publication
DOI: 10.4310/MRL.2002.V9.N6.A3
description: scientific article; zbMATH DE number 1930993