Recurrence formulas for Macdonald polynomials of type A

TL;DR

This paper derives explicit recurrence formulas for Macdonald polynomials of type A, enabling their decomposition in terms of specific basis elements related to fundamental weights.

Contribution

It provides explicit recurrence formulas and decomposition methods for Macdonald polynomials of type A based on fundamental weights.

Findings

Explicit decomposition formulas for Macdonald polynomials of type A.

Recurrence relations connecting different Macdonald polynomials.

Enhanced understanding of the structure of Macdonald polynomials.

Abstract

We consider products of two Macdonald polynomials of type A, indexed by dominant weights which are respectively a multiple of the first fundamental weight and a weight having zero component on the k-th fundamental weight. We give the explicit decomposition of any Macdonald polynomial of type A in terms of this basis.