Recurrence formulas for Macdonald polynomials of type A

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.

18 pages, LaTeX, revised version, to appear in Journal of Algebraic Combinatorics

References in corpus (1)

• Inversion of the Pieri formula for Macdonald polynomials

Cited by in corpus (3)

• Orthogonal polynomials of compact simple Lie groups: Branching rules for polynomials
• Multidimensional Matrix Inversions and Elliptic Hypergeometric Series on Root Systems
• An (inverse) Pieri formula for Macdonald polynomials of type C