A note on quotients of real algebraic groups by arithmetic subgroups

Abstract

Introduction Let G be a connected semi-simple algebraic group defined over Q. Let F be an arithmetic subgroup of G, i.e., a subgroup of G such that for some (and therefore any) faithful rational representation p: G--, GL(N, C) defined over Q, Fc~p-I(SL(N, Z)) is of finite index in both F and p-a(SL(N, Z)). Let K c G be a maximal compact subgroup of Ga, the set of real points of G. With this notation, we can state the main result of this note.