Commuting tuples in reductive groups and their maximal compact subgroups

Abstract

Let G be a reductive algebraic group and K G a maximal compact subgroup. We consider the representation spaces Hom.Z k ;K/ and Hom.Z k ;G/ with the topology induced from an embedding into K k and G k , respectively. The goal of this paper is to prove that Hom.Z k ;K/ is a strong deformation retract of Hom.Z k ;G/.