Isospectrality of Margulis–Smilga spacetimes for irreducible representations of real split semisimple Lie groups
Abstract
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.
Fields of Study & Subjects
Advanced Algebra and Geometry
Advanced Topics in Algebra
Nonlinear Waves and Solitons
Publication details
- Journal / source
- Algebraic & Geometric Topology
- Publisher
- Mathematical Sciences Publishers
- Volume
- 26
- Issue
- 2
- Pages
- 411–436
- Publication date
- 11 February 2026
- Language
- EN