Mathematische Zeitschrift

, Volume 269, Issue 1, pp 281–292

Pieri formulas for Macdonald’s spherical functions and polynomials

Article

DOI: 10.1007/s00209-010-0727-0

Cite this article as:
van Diejen, J.F. & Emsiz, E. Math. Z. (2011) 269: 281. doi:10.1007/s00209-010-0727-0

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.

Keywords

Symmetric functionsHall-Littlewood polynomialsMacdonald polynomialsPieri formulasRoot systemsReflection groups

Mathematics Subject Classification (2000)

Primary 05E05Secondary 33D5217B2220F55

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Instituto de Matemática y FísicaUniversidad de TalcaTalcaChile