On the Langlands type discrete groups. I: The Borel-Serre compactification (Q1098945)

In his fundamental paper ``On the functional equations satisfied by Eisenstein series'' [Lect. Notes Math. 544 (1976; Zbl 0332.10018)] \textit{R. P. Langlands} considered by various reasons a certain class of discrete subgroups of Lie groups which is larger than the class of arithmetically defined subgroups of (the group of real points of) reductive algebraic groups. In order to apply the theory of Eisenstein series to the study of the cohomology of these discrete groups (following an approach initiated by G. Harder and pursued by the reviewer [cf. e.g. \textit{G. Harder} in Discrete Subgroups of Lie Groups Appl. Moduli, Bombay 1973, 129-160 (1975; Zbl 0317.57022); \textit{J. Schwermer}, Kohomologie arithmetisch definierter Gruppen und Eisensteinreihen (Lect. Notes Math. 988, 1983; Zbl 0506.22015)]) the author extends the construction of the Borel-Serre compactification of the associated arithmetic locally symmetric spaces to this case. The underlying work of \textit{A. Borel} and \textit{J.-P. Serre} is in Comment. Math. Helv. 48, 436-491 (1973; Zbl 0274.22011).