## 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.## References

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## Bibliographic Information

**Jean-Philippe Burelle**- Affiliation: Département de mathématiques, Université de Sherbrooke, Sherbrooke, Quebec J1K 2R1, Canada
- MR Author ID: 987073
- ORCID: 0000-0003-2936-8901
- Email: j-p.burelle@usherbrooke.ca
**Sean Lawton**- Affiliation: Department of Mathematical Sciences, George Mason University, 4400 University Drive, Fairfax, Virginia 22030
- MR Author ID: 802618
- ORCID: 0000-0002-7186-3255
- Email: slawton3@gmu.edu
- Received by editor(s): January 31, 2022
- Received by editor(s) in revised form: August 8, 2022, and August 29, 2022
- Published electronically: November 3, 2022
- Additional Notes: The first author acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), RGPIN-2020-05557. The second author was partially supported by a Collaboration grant from the Simons Foundation.
- © Copyright 2022 American Mathematical Society
- Journal: Conform. Geom. Dyn.
**26**(2022), 194-207 - MSC (2020): Primary 14M35, 22D40, 20F18, 22F50; Secondary 14L30, 37A25
- DOI: https://doi.org/10.1090/ecgd/376
- MathSciNet review: 4504602