Dynamics on nilpotent character varieties
arXiv:2111.11922 · doi:10.1090/ecgd/376
Abstract
Let R(N,G) be the connected component of the identity of the variety of representations of a finitely generated nilpotent group N into a connected compact Lie group G, and let X(N,G) be the corresponding moduli space. We show that there exists a natural Out(N)-invariant measure on X(N,G) and that whenever Out(N) has at least one hyperbolic element, the action of Out(N) on X(N,G) is mixing with respect to this measure.
17 pages, Version 2 has minor updates and corrections, accepted for publication in Conformal Geometry and Dynamics