Article

Mathematische Zeitschrift

, Volume 269, Issue 1, pp 281-292

First online:

Pieri formulas for Macdonald’s spherical functions and polynomials

  • J. F. van DiejenAffiliated withInstituto de Matemática y Física, Universidad de Talca
  • , E. EmsizAffiliated withInstituto de Matemática y Física, Universidad de Talca Email author 

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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 functions Hall-Littlewood polynomials Macdonald polynomials Pieri formulas Root systems Reflection groups

Mathematics Subject Classification (2000)

Primary 05E05 Secondary 33D52 17B22 20F55