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arXiv · 2111.11922

Dynamics on nilpotent character varieties

Jean-Philippe Burelle·Sean Lawton
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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.

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Jean-Philippe Burelle, Sean Lawton. 2021-11-23. Dynamics on nilpotent character varieties. https://doi.org/10.1090/ecgd%2F376

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