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Pieri formulas for Macdonald’s spherical functions and polynomials

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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.

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Authors and Affiliations

  1. Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile

    J. F. van Diejen & E. Emsiz

Authors
  1. J. F. van Diejen
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  2. E. Emsiz
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Correspondence to E. Emsiz.

Additional information

Work supported in part by the Fondo Nacional de Desarrollo Científico y Tecnológico (FONDECYT) Grants # 1090118 and 3080006, by the Anillo ACT56 ‘Reticulados y Simetrías’ financed by the Comisión Nacional de Investigación Científica y Tecnológica (CONICYT), and by the Programa ‘Reticulados y Ecuaciones’ of the Universidad de Talca.

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van Diejen, J.F., Emsiz, E. Pieri formulas for Macdonald’s spherical functions and polynomials. Math. Z. 269, 281–292 (2011). https://doi.org/10.1007/s00209-010-0727-0

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  • DOI: https://doi.org/10.1007/s00209-010-0727-0

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