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A Pieri formula for Macdonald's spherical functions and polynomials (1009.4482v1)
Published 22 Sep 2010 in math.RT and math.CO
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.