On Harish-Chandra theory of global nonsymmetric functions

TL;DR

This paper extends Harish-Chandra theory to global nonsymmetric functions in the q,t-setting, providing a decomposition and explicit formulas, especially for the A1 case, advancing understanding of root systems.

Contribution

It introduces a Harish-Chandra-type decomposition for global nonsymmetric spherical functions in the q,t-framework, generalizing classical results to broader root systems.

Findings

Decomposition of nonsymmetric spherical functions in the q,t-setting.

Explicit formulas for the A1 case.

Generalization of the c-function to the q,t-context.

Abstract

This paper is devoted to the Harish-Chandra-type decomposition of the global nonsymmetric spherical functions in terms of their asymptotic expansions and the q,t-generalization of the celebrated c-function. This is for any reduced root systems in the q,t-setting; we pay special attention to the case of A1, where this decomposition is very explicit.