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<p>In this paper, we propose a family 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 relative Langlands duality framework. For the proposed relative trace formula comparisons associated to some strongly tempered spherical varieties, we prove the fundamental lemma and smooth transfer in the <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi>p</mi> </math></EquationSource> <EquationSource Format="TEX">$p$</EquationSource> </InlineEquation>-adic case. Moreover, inspired by the period integral conjecture in the relative Langlands duality, we propose a conjecture regarding degenerate Whittaker periods, which generalizes Lapid-Mao’s conjecture of the Whittaker period.</p>

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Relative Langlands duality for some strongly tempered spherical varieties

  • 期刊论文

  • 发表日期：

    2025年11月11日

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  • Zhengyu Mao,
  • Chen Wan,
  • Lei Zhang

摘要

In this paper, we propose a family 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 relative Langlands duality framework. For the proposed relative trace formula comparisons associated to some strongly tempered spherical varieties, we prove the fundamental lemma and smooth transfer in the p $p$ -adic case. Moreover, inspired by the period integral conjecture in the relative Langlands duality, we propose a conjecture regarding degenerate Whittaker periods, which generalizes Lapid-Mao’s conjecture of the Whittaker period.