Transfer of characters for discrete series representations of the unitary groups in the equal rank case via the Cauchy-Harish-Chandra integral
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866917289155100672 |
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| author | Merino, Allan |
| author_facet | Merino, Allan |
| contents | As conjectured by T. Przebinda, the transfer of characters in the Howe's correspondence should be obtained via the Cauchy-Harish-Chandra integral. In this paper, we prove that the conjecture holds for the dual pair $(G = U(p, q), G' = U(r, s))$, $p+q = r+s$, starting with a discrete series representation $Π$ of $\widetilde{U}(p, q)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2101_02063 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Transfer of characters for discrete series representations of the unitary groups in the equal rank case via the Cauchy-Harish-Chandra integral Merino, Allan Representation Theory 22E45 (Primary), 22E46, 22E30 (Secondary) As conjectured by T. Przebinda, the transfer of characters in the Howe's correspondence should be obtained via the Cauchy-Harish-Chandra integral. In this paper, we prove that the conjecture holds for the dual pair $(G = U(p, q), G' = U(r, s))$, $p+q = r+s$, starting with a discrete series representation $Π$ of $\widetilde{U}(p, q)$. |
| title | Transfer of characters for discrete series representations of the unitary groups in the equal rank case via the Cauchy-Harish-Chandra integral |
| topic | Representation Theory 22E45 (Primary), 22E46, 22E30 (Secondary) |
| url | https://arxiv.org/abs/2101.02063 |