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Article Dans Une Revue Journal of Number Theory Année : 2022

Multiplicities and Plancherel formula for the space of nondegenerate Hermitian matrices

Résumé

This paper contains two results concerning the spectral decomposition, in a broad sense, of the space of nondegenerate Hermitian matrices over a local field of characteristic zero. The first is an explicit Plancherel decomposition of the associated $L^2$ space thus confirming a conjecture of Sakellaridis-Venkatesh in this particular case. The second is a formula for the multiplicities of generic representations in the $p$-adic case that extends previous work of Feigon-Lapid-Offen. Both results are stated in terms of Arthur-Clozel's quadratic local base-change and the proofs are based on local analogs of two relative trace formulas previously studied by Jacquet and Ye and known as (relative) Kuznetsov trace formulas.
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hal-02989477 , version 1 (05-01-2024)

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Paternité - Pas d'utilisation commerciale

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Raphaël Beuzart-Plessis. Multiplicities and Plancherel formula for the space of nondegenerate Hermitian matrices. Journal of Number Theory, 2022, 230, ⟨10.1016/j.jnt.2021.06.001⟩. ⟨hal-02989477⟩
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