Vector-valued Gelfand-Kazhdan criterion
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915763745456128 |
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| author | Chen, Fulin Sun, Binyong Weng, Yixiang |
| author_facet | Chen, Fulin Sun, Binyong Weng, Yixiang |
| contents | The Gelfand-Kazhdan criterion is a fundamental tool for studying multiplicity-one properties of local periods of representations. However, it does not apply to many cases arising in the relative Langlands program. Generalizing the usual Gelfand-Kazhdan criterion, we formulate and prove a vector-valued Gelfand-Kazhdan criterion that fits into the general framework of the relative Langlands program. As an illustration of its effectiveness, we establish the multiplicity-one property for the local Asai Rankin-Selberg periods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_23199 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Vector-valued Gelfand-Kazhdan criterion Chen, Fulin Sun, Binyong Weng, Yixiang Representation Theory The Gelfand-Kazhdan criterion is a fundamental tool for studying multiplicity-one properties of local periods of representations. However, it does not apply to many cases arising in the relative Langlands program. Generalizing the usual Gelfand-Kazhdan criterion, we formulate and prove a vector-valued Gelfand-Kazhdan criterion that fits into the general framework of the relative Langlands program. As an illustration of its effectiveness, we establish the multiplicity-one property for the local Asai Rankin-Selberg periods. |
| title | Vector-valued Gelfand-Kazhdan criterion |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2601.23199 |