# Notes on a conjecture of Braverman-Kazhdan

## TL;DR

This paper provides an explicit formula and geometric interpretation for the Fourier kernel associated with an exotic Fourier operator on finite groups of algebraic groups, advancing understanding of Braverman-Kazhdan's conjecture.

## Contribution

It offers a concrete formula and geometric insight into the Fourier kernel, supporting Braverman and Kazhdan's conjecture under certain assumptions.

## Key findings

- Explicit formula for the Fourier kernel
- Geometric interpretation of the Fourier kernel
- Support for Braverman-Kazhdan's conjecture under assumptions

## 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).