A Pieri formula for Macdonald's spherical functions and polynomials
J. F. van Diejen, E. Emsiz
TL;DR
This paper derives explicit Pieri formulas for Macdonald's spherical functions and polynomials, generalizing known formulas for special cases and providing tools for their computation in root systems.
Contribution
It introduces a new explicit Pieri formula for Macdonald's spherical functions and polynomials applicable to general root systems, extending previous results.
Findings
Pieri formulas explicitly derived for Macdonald's spherical functions
Formulas recover classical cases for type A root systems
Provides a unified approach to Macdonald polynomials and spherical functions
Abstract
We present explicit Pieri formulas for Macdonald's spherical functions (or generalized Hall-Littlewood polynomials associated with root systems) and their -deformation the Macdonald polynomials. For the root systems of type , 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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