Orthogonality of Macdonald polynomials with unitary parameters

TL;DR

This paper establishes discrete orthogonality relations for Macdonald polynomials with unitary parameters across various root systems, advancing the understanding of their algebraic and analytical properties.

Contribution

It introduces new orthogonality relations for Macdonald polynomials with parameters on the unit circle, applicable to all admissible root systems.

Findings

Discrete orthogonality relations proved for Macdonald polynomials

Applicable to all admissible irreducible root systems

Parameters are on the unit circle with truncation conditions

Abstract

For any admissible pair of irreducible reduced crystallographic root systems, we present discrete orthogonality relations for a finite-dimensional system of Macdonald polynomials with parameters on the unit circle subject to a truncation relation.