Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916938216636416 |
|---|---|
| author | Lutsko, Christopher Weich, Tobias Wolf, Lasse L. |
| author_facet | Lutsko, Christopher Weich, Tobias Wolf, Lasse L. |
| contents | Given a real semisimple connected Lie group $G$ and a discrete subgroup $Γ< G$ we prove a precise connection between growth rates of the group $Γ$, polyhedral bounds on the joint spectrum of the ring of invariant differential operators, and the decay of matrix coefficients. In particular, this allows us to completely characterize temperedness of $L^2(Γ\backslash G)$ in terms of Quint's growth indicator function. As an application of our sharp polyhedral bounds we prove temperedness of $L^2(Γ\backslash G)$ for all Borel Anosov subgroups $Γ$ in higher rank Lie groups $G$ not locally isomorphic to $\mathfrak{sl}_3(\mathbb{K}),\mathbb{K}=\R,\C,\mathbb H,$ or $\mathfrak{e}_{6(-26)}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02530 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces Lutsko, Christopher Weich, Tobias Wolf, Lasse L. Representation Theory 22E46, 58C40 Given a real semisimple connected Lie group $G$ and a discrete subgroup $Γ< G$ we prove a precise connection between growth rates of the group $Γ$, polyhedral bounds on the joint spectrum of the ring of invariant differential operators, and the decay of matrix coefficients. In particular, this allows us to completely characterize temperedness of $L^2(Γ\backslash G)$ in terms of Quint's growth indicator function. As an application of our sharp polyhedral bounds we prove temperedness of $L^2(Γ\backslash G)$ for all Borel Anosov subgroups $Γ$ in higher rank Lie groups $G$ not locally isomorphic to $\mathfrak{sl}_3(\mathbb{K}),\mathbb{K}=\R,\C,\mathbb H,$ or $\mathfrak{e}_{6(-26)}$. |
| title | Polyhedral bounds on the joint spectrum and temperedness of locally symmetric spaces |
| topic | Representation Theory 22E46, 58C40 |
| url | https://arxiv.org/abs/2402.02530 |