BZSV Duality for Some Strongly Tempered Spherical Varieties

2023/10/27 by Mao, Zhengyu, Wan, Chen, Zhang, Lei · 1 citation
#22E30 22E35 22E50 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2310.17837

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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