Pieri formulas for Macdonald’s spherical functions and polynomials
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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.
KeywordsSymmetric functions Hall-Littlewood polynomials Macdonald polynomials Pieri formulas Root systems Reflection groups
Mathematics Subject Classification (2000)Primary 05E05 Secondary 33D52 17B22 20F55
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