A Note On Nilpotent Representations

Lior Silberman, Maxime Bergeron

Abstract: Let Γ be a finitely generated nilpotent group and let G be a complex reductive algebraic group. The representation variety Hom(Γ,G) and the character variety Hom(Γ,G)//G each carry a natural topology, and we describe the topology of their connected components in terms of representations factoring through quotients of Γ by elements of its lower central series.