论文标题
Margulis-Smilga空间的同一镜头，用于真实分裂半元素lie群的不可还原表示
Isospectrality of Margulis-Smilga spacetimes for irreducible representations of real split semisimple Lie groups
论文作者
论文摘要
在本文中，我们查看了带有微不足道的中心和忠实的不可记述的代数表示$ \ nathtt {r} $ of $ \ mathsf {g mathsf {g} $在某些矢量空间$ \ mathsf {v} $中的extrients serifient和siveriation，siverage serag和sivernage of afloge serag和siverrient，我们会介绍一个sefient-nefient-aftermant，我们会介绍实际的serfient，否则seragient和spocor， $ \ mathsf {psl}（n，\ mathbb {r}）$的$）。 我们表明，存在$（g，x）\ in \ Mathsf {g} \ ltimes_ \ Mathtt {r} \ Mathsf {v} $的$（g，x）\ in Margulis forpariants制成的多项式。此外，我们表明，$ \ mathsf {g} \ ltimes_ \ Mathtt {r} \ Mathsf {V} $的任何Zariski密集生成的子组，对于非遗相元素的线性部分是loxodromic的线性部分，与Margulis Invariant相关。特别是，我们表明Margulis- Smilga的空间也是异常的僵化。
In this article, we look at real split semisimple algebraic groups $\mathsf{G}$ with trivial center and faithful irreducible algebraic representations $\mathtt{R}$ of $\mathsf{G}$ on some vector space $\mathsf{V}$ which admit zero as a weight and which are self-contragredient (for example, adjoint representation of $\mathsf{PSL}(n,\mathbb{R})$). We show that, there exist polynomials made out of Margulis invariants of $(g,X)\in\mathsf{G}\ltimes_\mathtt{R}\mathsf{V}$ which are also rational expressions in $(g,X)$. Moreover, we show that any Zariski dense finitely generated subgroup of $\mathsf{G}\ltimes_\mathtt{R}\mathsf{V}$, for which the linear parts of the non-identity elements are loxodromic, is isospectrally rigid with respect to the Margulis invariants. In particular, we show that Margulis--Smilga spacetimes are isospectrally rigid too.
