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BC-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials

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arxiv q-alg/9611011 v2 pith:VTFDDKIR submitted 1996-11-11 q-alg math.QA

Andrei Okounkov This is my paper · ORCID
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keywords polynomialsformulabinomialinterpolationkoornwindermacdonaldparametricprove
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We consider 3-parametric polynomials which replace the A-series interpolation Macdonald polynomials in the BC case. For these polynomials, we prove: an integral representation, a combinatorial formula, Pieri-type rules, Cauchy identity, and we also show that they do not satisfy any rational q-difference equation. We also prove a binomial formula for the 6-parametric Koornwinder polynomials.

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  1. Vogel's universality and Macdonald dimensions

    hep-th 2025-07 conditional novelty 4.0 of 10

    The paper gives a single rational formula for adjoint Macdonald dimensions that unifies the simply laced Lie algebras A_n, D_n, E6, E7, E8, plus explicit mixed-root-system dimension formulas.

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