Compactifications of symmetric and locally symmetric spaces (Q1812518)

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.