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arXiv · 2310.17837

BZSV Duality for Some Strongly Tempered Spherical Varieties

Zhengyu Mao·Chen Wan·Lei Zhang
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Abstract

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

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Zhengyu Mao, Chen Wan, Lei Zhang. 2024-03-05. BZSV Duality for Some Strongly Tempered Spherical Varieties. https://arxiv.org/abs/2310.17837

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