Special affine representations for hyperbolic groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866909120471236608 |
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| author | Boucher, Kevin |
| author_facet | Boucher, Kevin |
| contents | In this paper we extend the construction of special representations to Gromov hyperbolic groups which admits complementary series. We prove that these representations have a natural non-trivial reduced cohomology class $[c]$. An analogue of Kuhn-Vershik's formula is established and as a by-product a characterisation of hyperbolic groups that admit complementary series. Investigating dynamical properties of the cohomology class $[c]$ we prove an cocycle equidistribution theorem á la Roblin-Margulis and deduce the irreducibility of the associated affine actions. The irreducibility of the affine actions associated to the canonical class $[c]$ is original even in the case of uniform lattices in $SO(n,1)$, $SU(n,1)$ or $SL_2(\mathbb{Q}_p)$ with $n\ge 1$ and $p$ prime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_00427 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Special affine representations for hyperbolic groups Boucher, Kevin Group Theory Dynamical Systems Operator Algebras 20F67 22D10 37A46 In this paper we extend the construction of special representations to Gromov hyperbolic groups which admits complementary series. We prove that these representations have a natural non-trivial reduced cohomology class $[c]$. An analogue of Kuhn-Vershik's formula is established and as a by-product a characterisation of hyperbolic groups that admit complementary series. Investigating dynamical properties of the cohomology class $[c]$ we prove an cocycle equidistribution theorem á la Roblin-Margulis and deduce the irreducibility of the associated affine actions. The irreducibility of the affine actions associated to the canonical class $[c]$ is original even in the case of uniform lattices in $SO(n,1)$, $SU(n,1)$ or $SL_2(\mathbb{Q}_p)$ with $n\ge 1$ and $p$ prime. |
| title | Special affine representations for hyperbolic groups |
| topic | Group Theory Dynamical Systems Operator Algebras 20F67 22D10 37A46 |
| url | https://arxiv.org/abs/2012.00427 |