论文标题
双曲线组的特殊仿射表示
Special affine representations for hyperbolic groups
论文作者
论文摘要
在本文中，我们将特殊代表的构造扩展到了接受补充系列的Gromov双曲线群体。我们证明，这些表示形式具有自然的非平凡的同胞级$ [C] $。建立了Kuhn-Vershik公式的类似物，并作为副产品的表征，是辅助系列的双曲线群体的特征。调查了共同体类$ [c] $的动力学特性，我们证明了共同分布定理Álala Roblin-margulis，并推断出相关的仿射作用的不可约性。即使在$（n，1）$，$ su（n，1）$（n，1）$或$ sl_2（\ MathBB {q} _p）$的情况下，与规范类$ [C] $相关的仿射动作的不可约性也是原始的。
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.
