A reduction formula for the Dunkl kernel for the root systems of type $A$

TL;DR

This paper derives a reduction formula for the Dunkl kernel associated with root systems of type A, expressing it recursively via lower-dimensional kernels, and provides a related formula for the intertwining operator V_k.

Contribution

It introduces a recursive reduction formula for the Dunkl kernel of type A root systems and the intertwining operator, simplifying their computation.

Findings

Dunkl kernel for A_n expressed as an integral involving A_{n-1}

Reduction formula for the intertwining operator V_k for type A

Facilitates recursive computation of Dunkl kernels

Abstract

In this paper, we provide a reduction formula for the Dunkl kernel for the root systems of type $A$. The Dunkl kernel for the root system $A_n$ is expressed as an integral involving the Dunkl kernel for the root system $A_{n-1}$. The corresponding reduction formula for the intertwining operator $V_k$ is given.