Multiplicities and Plancherel formula for the space of nondegenerate\n Hermitian matrices

2020/08/11 by Raphaël Beuzart-Plessis, Beuzart-Plessis, Raphaël
Chemistry · Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Molecular spectroscopy and chirality #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2008.05036

openalex publication_date 2020/08/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper contains two results concerning the spectral decomposition, in a\nbroad sense, of the space of nondegenerate Hermitian matrices over a local\nfield of characteristic zero. The first is an explicit Plancherel decomposition\nof the associated L² space thus confirming a conjecture of\nSakellaridis-Venkatesh in this particular case. The second is a formula for the\nmultiplicities of generic representations in the p-adic case that extends\nprevious work of Feigon-Lapid-Offen. Both results are stated in terms of\nArthur-Clozel's quadratic local base-change and the proofs are based on local\nanalogs of two relative trace formulas previously studied by Jacquet and Ye and\nknown as (relative) Kuznetsov trace formulas.\n

Citations

• On Euler Products and the Classification of Automorphic Representations I
• A `relative' local Langlands correspondence

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