Recurrence formulas for Macdonald polynomials of type A

Michel Lassalle (1) , Michael J. Schlosser

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

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 kth fundamental weight. We give the explicit decomposition of any Macdonald polynomial of type A in terms of this basis.

Domaines: Physique mathématique [math-ph]

Michel Lassalle, Michael J. Schlosser. Recurrence formulas for Macdonald polynomials of type A. Journal of Algebraic Combinatorics, 2010, 32 (1), pp.113--131. ⟨10.1007/s10801-009-0207-y⟩. ⟨hal-00693447⟩