Representation Equivalence of Lattices in Lie Groups
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915551288229888 |
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| author | Bhagwat, Chandrasheel Mondal, Kaustabh |
| author_facet | Bhagwat, Chandrasheel Mondal, Kaustabh |
| contents | Let $Γ_1$ and $Γ_2$ 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 $L^2(Γ_1 \backslash G)$ and $L^2(Γ_2 \backslash G)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00294 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Representation Equivalence of Lattices in Lie Groups Bhagwat, Chandrasheel Mondal, Kaustabh Representation Theory Group Theory Number Theory 22E40, 22E45, 53C35 Let $Γ_1$ and $Γ_2$ 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 $L^2(Γ_1 \backslash G)$ and $L^2(Γ_2 \backslash G)$ 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. |
| title | Representation Equivalence of Lattices in Lie Groups |
| topic | Representation Theory Group Theory Number Theory 22E40, 22E45, 53C35 |
| url | https://arxiv.org/abs/2309.00294 |