A spectral theorem for compact representations and non-unitary cusp forms
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929226996776960 |
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| author | Deitmar, Anton |
| author_facet | Deitmar, Anton |
| contents | We show that a compact representation of a semisimple Lie group has an orthogonal decomposition into finite length representations. This generalises and simplifies a number of more special spectral theorems in the literature. We apply it to the case of cusp forms, thus settling the spectral theory for the space of non-unitary twisted cusp forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01859 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A spectral theorem for compact representations and non-unitary cusp forms Deitmar, Anton Number Theory 11F72 We show that a compact representation of a semisimple Lie group has an orthogonal decomposition into finite length representations. This generalises and simplifies a number of more special spectral theorems in the literature. We apply it to the case of cusp forms, thus settling the spectral theory for the space of non-unitary twisted cusp forms. |
| title | A spectral theorem for compact representations and non-unitary cusp forms |
| topic | Number Theory 11F72 |
| url | https://arxiv.org/abs/2401.01859 |