Dynamics on nilpotent character varieties

Burelle, Jean-Philippe; Lawton, Sean

doi:10.1090/ecgd/376

Dynamics on nilpotent character varieties
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by Jean-Philippe Burelle and Sean Lawton

Conform. Geom. Dyn. 26 (2022), 194-207

DOI: https://doi.org/10.1090/ecgd/376

Published electronically: November 3, 2022

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Abstract:

Let $\mathsf {Hom}^{0}(\Gamma ,G)$ be the connected component of the identity of the variety of representations of a finitely generated nilpotent group $\Gamma$ into a connected compact Lie group $G$, and let $\mathsf {X}^0(\Gamma ,G)$ be the corresponding moduli space. We show that there exists a natural $\mathsf {Out}(\Gamma )$-invariant measure on $\mathsf {X}^0(\Gamma ,G)$ and that whenever $\mathsf {Out}(\Gamma )$ has at least one hyperbolic element, the action of $\mathsf {Out}(\Gamma )$ on $\mathsf {X}^0(\Gamma , G)$ is mixing with respect to this measure.

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