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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2501.11917 |
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| _version_ | 1866909462840737792 |
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| author | Geng, Zhibin |
| author_facet | Geng, Zhibin |
| contents | Let $\K$ be an archimedean local field. We investigate the existence of the twisted Shalika functionals on irreducible admissible smooth representations of $\GL_{2n}(\K)$ in terms of their L-parameters. As part of our proof, we establish a Hochschild-Serre spectral sequence for nilpotent normal subgroups and a Kunneth formula in the framework of Schwartz homology. We also prove the analogous result for twisted linear periods using theta correspondence. The existence of twisted Shalika functionals on representations of $\GL_{2n}^{+}(\R)$ is also studied, which is of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11917 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the existence of twisted Shalika periods: the Archimedean case Geng, Zhibin Representation Theory Let $\K$ be an archimedean local field. We investigate the existence of the twisted Shalika functionals on irreducible admissible smooth representations of $\GL_{2n}(\K)$ in terms of their L-parameters. As part of our proof, we establish a Hochschild-Serre spectral sequence for nilpotent normal subgroups and a Kunneth formula in the framework of Schwartz homology. We also prove the analogous result for twisted linear periods using theta correspondence. The existence of twisted Shalika functionals on representations of $\GL_{2n}^{+}(\R)$ is also studied, which is of independent interest. |
| title | On the existence of twisted Shalika periods: the Archimedean case |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2501.11917 |