Dynamics on nilpotent character varieties

Let H mathvariant="sans-serif">o mathvariant="sans-serif">m 0 ( mathvariant="normal">Γ , G stretchy="false">) \mathsf {Hom}^{0}(\Gamma ,G) be the connected component of identity variety representations a finitely generated nilpotent group alttext="normal Gamma"> encoding="application/x-tex">\Gamma into compact Lie alttext="upper G"> encoding="application/x-tex">G , and let X mathvariant="sans-serif">X {X}^0(\Gamma corresponding moduli space. We show that there exists natural O u t mathvariant="sans-serif">O mathvariant="sans-serif">u mathvariant="sans-serif">t {Out}(\Gamma ) -invariant measure on whenever has at least one hyperbolic element, action , G) is mixing with respect to this measure.