A weak kernel formula for Bessel functions

TL;DR

This paper establishes a weak kernel formula for Bessel functions associated with irreducible generic representations of p-adic GL(n), and shows the equivalence of two definitions of Bessel functions in this context.

Contribution

It introduces a weak kernel formula for Bessel functions and proves the coincidence of Bessel functions defined by distribution and Whittaker models.

Findings

Proved a weak kernel formula for Bessel functions.

Established the equivalence of Bessel functions from different definitions.

Abstract

In this paper, we prove a weak kernel formula of Bessel functions attached to irreducible generic representations of p-adic $GL(n)$. As an application, we show that the Bessel function defined by Bessel distribution coincides with the Bessel function defined via uniqueness of Whittaker models on the open Bruhat cell.