Recurrence formulas for Macdonald polynomials of type A

Michel Lassalle, Michael J. Schlosser

Published 2009-02-12, updated 2009-10-10Version 2

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.