Notes on a conjecture of Braverman-Kazhdan

2019/06/18 by Gérard Laumon, Laumon, Gérard, Emmanuel Letellier +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1906.07476

openalex publication_date 2019/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a connected reductive algebraic group G over a finite field together with a representation of the dual group of G in GL(n), Braverman and Kazhdan defined an exotic Fourier operator on the space of complex valued functions on the finite group of rational points of G. In these notes we give an explicit formula for the Fourier kernel and a geometrical interpretation of this formula (as conjectured by Braverman and Kazhdan under some assumption).

Cited by

• On Jacobi sums arising from the classical doubling method

Related

• Fourier transform from the symmetric square representation of PGL₂ and SL₂
• On the conjectures of Braverman-Kazhdan
• The ρ-Fourier transform
• Trace Paley-Wiener theorem for Braverman-Kazhdan's asymptotic Hecke algebra
• Non-linear Fourier transforms and the Braverman-Kazhdan conjecture