标题： 双曲群的特殊仿射表示 显示英文标题

标题： Special affine representations for hyperbolic groups

摘要： 在本文中，我们将特殊表示的构造扩展到允许补序列的Gromov双曲群。我们证明这些表示具有自然的非平凡约化上同调类$[c]$。建立了Kuhn-Vershik公式的一个类似形式，并作为副产品给出了允许补序列的双曲群的特征。研究上同调类$[c]$的动力学性质，我们证明了一个类似Roblin-Margulis的上循环等分布定理，并推导出相关仿射作用的不可约性。 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. 显示英文摘要

摘要： 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 \'a 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.