Abstract
We consider 3-parametric polynomialsP *μ (x; q, t, s) which replace theA n-series interpolation Macdonald polynomialsP *μ (x; q, t) for theBC n-type root system. For these polynomials we prove an integral representation, a combinatorial formula, Pieri rules, Cauchy identity, and we also show that they do not satisfy any rationalq-difference equation. Ass → ∞ the polynomialsP *μ (x; q, t, s) becomeP *μ (x; q, t). We also prove a binomial formula for 6-parametric Koornwinder polynomials.
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Okounkov, A. BC-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials. Transformation Groups 3, 181–207 (1998). https://doi.org/10.1007/BF01236432
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DOI: https://doi.org/10.1007/BF01236432