A Pieri formula for Macdonald's spherical functions and polynomials

Abstract

We present explicit Pieri formulas for Macdonald's spherical functions (or generalized Hall-Littlewood polynomials associated with root systems) and their $q$-deformation the Macdonald polynomials. For the root systems of type $A$, our Pieri formulas recover the well-known Pieri formulas for the Hall-Littlewood and Macdonald symmetric functions due to Morris and Macdonald as special cases.

11 pages. To appear in Math. Z

References in corpus (3)

• Inversion of the Pieri formula for Macdonald polynomials
• Scattering theory of discrete (pseudo) Laplacians on a Weyl chamber
• An (inverse) Pieri formula for Macdonald polynomials of type C

Cited by in corpus (1)

• Unitary representations of affine Hecke algebras related to Macdonald spherical functions