Involutions of double affine Hecke algebras

TL;DR

This paper investigates the symmetrical structure of double affine Hecke algebras, focusing on their commutative subalgebras, which is crucial for understanding intertwiners within this algebraic framework.

Contribution

It formulates and proves a key structural result that enables symmetric treatment of the two commutative subalgebras in double affine Hecke algebras.

Findings

Established a structural theorem for double affine Hecke algebras

Demonstrated the symmetric role of two commutative subalgebras

Enhanced understanding of intertwiners in the algebraic context

Abstract

The main aim of the paper is to formulate and prove a result about the structure of double affine Hecke algebras which allows its two commutative subalgebras to play a symmetric role. This result is essential for the theory of intertwiners of double affine Hecke algebras.