Nonabelian Fourier Kernels on SL₂ and GL₂

2024/09/23 by Zhilin Luo, Luo, Zhilin, Ngô Bảo Châu +1
Mathematics · #Advanced Algebra and Geometry #Advanced Harmonic Analysis Research #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2409.14696

openalex publication_date 2024/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For G=SL₂ or GL₂, we present explicit formulas for the nonabelian Fourier kernels on G, as conjectured by A. Braverman and D. Kazhdan. Additionally, we furnish explicit formulas for the orbital Hankel transform on G, a topic investigated by the second author, and provide an explicit formula for the stable orbital integral of the basic function. These results are applicable to local fields with residual characteristics other than two.

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