Theta correspondence via group C*-algebras
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929622606675968 |
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| author | Goffeng, Magnus Mesland, Bram Sengun, Mehmet Haluk |
| author_facet | Goffeng, Magnus Mesland, Bram Sengun, Mehmet Haluk |
| contents | We prove that the well-known explicit construction of the local theta correspondence by Li has a simple interpretation in terms of group C*-algebras. In particular, we deduce that in two standard cases where Li's method work, local theta correspondence arises from a continuous functor. Moreover, using results from a companion paper, we treat global theta correspondence using C*-algebraic methods. As a byproduct, we exhibit that Rallis inner product formula can be interpreted as a certain natural inclusion being an isometry. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_07501 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Theta correspondence via group C*-algebras Goffeng, Magnus Mesland, Bram Sengun, Mehmet Haluk Operator Algebras Number Theory Representation Theory 11F27, 22E50, 22E55, 22D25, 46L08 We prove that the well-known explicit construction of the local theta correspondence by Li has a simple interpretation in terms of group C*-algebras. In particular, we deduce that in two standard cases where Li's method work, local theta correspondence arises from a continuous functor. Moreover, using results from a companion paper, we treat global theta correspondence using C*-algebraic methods. As a byproduct, we exhibit that Rallis inner product formula can be interpreted as a certain natural inclusion being an isometry. |
| title | Theta correspondence via group C*-algebras |
| topic | Operator Algebras Number Theory Representation Theory 11F27, 22E50, 22E55, 22D25, 46L08 |
| url | https://arxiv.org/abs/2412.07501 |