Cycles for asymptotic solutions and Weyl group

TL;DR

This paper describes cycles for asymptotic solutions of the Heckman-Opdam hypergeometric system of type A_n, enumerates them by the symmetric group, and calculates key asymptotic and integral values.

Contribution

It introduces a new description of cycles for asymptotic solutions and computes associated asymptotic coefficients and integrals, advancing understanding of hypergeometric systems.

Findings

Cycles are enumerated by elements of the symmetric group

Leading asymptotic and coefficients are explicitly calculated

Certain multiple integrals over special cycles are evaluated

Abstract

In this paper cycles for asymptotic solutions for Heckman-Opdam hypergeometric system of type $A_n$ are described. Cycles are enumerated by elements of symmetric group. Leading asymptotic and leading coefficient are calculated. Value of certain multiple integral over special cycles is calculated with the help of result of Opdam.