On certain identities between Fourier transforms of weighted orbital integrals on infinitesimal symmetric spaces of Guo-Jacquet

2024/10/31 by Huajie Li, Li, Huajie
Mathematics · #Advanced Algebra and Geometry #Advanced Harmonic Analysis Research #FOS: Mathematics #Mathematical Analysis and Transform Methods #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2410.23648

openalex publication_date 2024/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In an infinitesimal variant of Guo-Jacquet trace formulae, the regular semi-simple terms are expressed as noninvariant weighted orbital integrals on two global infinitesimal symmetric spaces. We prove some relations between the Fourier transforms of invariant weighted orbital integrals on the corresponding local infinitesimal symmetric spaces. These relations should be useful in the noninvariant comparison of the infinitesimal variant of Guo-Jacquet trace formulae.

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