Isospectrality of Margulis–Smilga spacetimes for irreducible representations of real split semisimple Lie groups

Ghosh, Sourav

doi:10.2140/agt.2026.26.411

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Isospectrality of Margulis–Smilga spacetimes for irreducible representations of real split semisimple Lie groups

Sourav Ghosh

Algebraic & Geometric Topology 26 (2026) 411–436

DOI: 10.2140/agt.2026.26.411

Abstract

We look at real split semisimple algebraic groups $G$ with trivial center and faithful irreducible algebraic representations $R$ of $G$ on some vector space $V$ which admit zero as a weight and which are self-contragredient (for example, adjoint representations of $P S L (n, ℝ)$ ).

We show that there exist polynomials made out of Margulis invariants of $(g, X) \in G ⋉_{R} V$ which are also rational expressions in $(g, X)$ . Moreover, we show that any Zariski dense finitely generated subgroup of $G ⋉_{R} V$ , for which the linear parts of the nonidentity elements are loxodromic, is isospectrally rigid with respect to the Margulis invariants. In particular, we show that Margulis–Smilga spacetimes are isospectrally rigid too.

Keywords

Margulis invariants, isospectral rigidity

Mathematical Subject Classification

Primary: 22E40, 53C24

References

Publication

Received: 30 October 2022

Revised: 9 February 2025

Accepted: 23 March 2025

Published: 11 February 2026

Authors

Sourav Ghosh
Department of Mathematics Ashoka University Sonipat India

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Volume 26, issue 2 (2026)