Transformation Groups

, Volume 3, Issue 2, pp 181-207

First online:

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

  • A. OkounkovAffiliated withDepartment of Mathematics, University of Chicago

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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.