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arXiv · 2309.00294

Representation Equivalence of Lattices in Lie Groups

Chandrasheel Bhagwat·Kaustabh Mondal
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Abstract

Let $\Gamma_1$ and $\Gamma_2$ be two lattices of finite covolume in a semisimple Lie group $G$. We prove a spectral rigidity result for the representation spectra of the right regular representations $L^2(\Gamma_1 \backslash G)$ and $L^2(\Gamma_2 \backslash G)$ of $G$. This can be thought of as an analogue of the strong multiplicity one theorem and it generalises a result by the first author and Rajan to the case of non-uniform lattices.

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BibTeXRIS

Chandrasheel Bhagwat, Kaustabh Mondal. 2023-09-01. Representation Equivalence of Lattices in Lie Groups. https://arxiv.org/abs/2309.00294

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