BZSV Duality for Some Strongly Tempered Spherical Varieties
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917604203954176 |
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| author | Mao, Zhengyu Wan, Chen Zhang, Lei |
| author_facet | Mao, Zhengyu Wan, Chen Zhang, Lei |
| contents | We propose two families of relative trace formula comparisons in the study of relative Langlands duality conjectured by Ben-Zvi--Sakellaridis--Venkatesh. This allows us to incorporate numerous relative trace formula comparisons studied during the last four decades under the BZSV duality framework. For the proposed relative trace formula comparisons associated to some strongly tempered spherical varieties, we will prove the fundamental lemma and smooth transfer in the $p$-adic case. Moreover, inspired by the BZSV duality conjecture, we propose a conjecture regarding the degenerate Whittaker period, which generalizes Lapid-Mao's conjecture of the Whittaker period |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_17837 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | BZSV Duality for Some Strongly Tempered Spherical Varieties Mao, Zhengyu Wan, Chen Zhang, Lei Number Theory Representation Theory 22E30 22E35 22E50 We propose two families of relative trace formula comparisons in the study of relative Langlands duality conjectured by Ben-Zvi--Sakellaridis--Venkatesh. This allows us to incorporate numerous relative trace formula comparisons studied during the last four decades under the BZSV duality framework. For the proposed relative trace formula comparisons associated to some strongly tempered spherical varieties, we will prove the fundamental lemma and smooth transfer in the $p$-adic case. Moreover, inspired by the BZSV duality conjecture, we propose a conjecture regarding the degenerate Whittaker period, which generalizes Lapid-Mao's conjecture of the Whittaker period |
| title | BZSV Duality for Some Strongly Tempered Spherical Varieties |
| topic | Number Theory Representation Theory 22E30 22E35 22E50 |
| url | https://arxiv.org/abs/2310.17837 |