Transformation Groups

, Volume 3, Issue 2, pp 181–207

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

Authors

  • A. Okounkov
    • Department of MathematicsUniversity of Chicago
Article

DOI: 10.1007/BF01236432

Cite this article as:
Okounkov, A. Transformation Groups (1998) 3: 181. doi:10.1007/BF01236432

Abstract

We consider 3-parametric polynomialsPμ*(x; q, t, s) which replace theAn-series interpolation Macdonald polynomialsPμ*(x; q, t) for theBCn-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 polynomialsPμ*(x; q, t, s) becomePμ*(x; q, t). We also prove a binomial formula for 6-parametric Koornwinder polynomials.

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Copyright information

© Birkhäuser 1998