A Pieri formula for Macdonald's spherical functions and polynomials

Details A Pieri formula for Macdonald's spherical functions and polynomials A Pieri formula for Macdonald's spherical functions and polynomials

2010-09-22

arxiv.org/abs/1009.4482v1

Mathematische Zeitschrift, Volume 269, Issue 1 (2011), Page 281-292

Mathematics

Representation Theory

11 pages. To appear in Math. Z

Scientific paper

10.1007/s00209-010-0727-0

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.

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