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

A. Okounkov

Research output: Contribution to journalArticlepeer-review

39 Citations (Scopus)

Abstract

We consider 3-parametric polynomials P*μ(cursive Greek chi; q, t, s) which replace the An-series interpolation Macdonald polynomials P*μ(cursive Greek chi; q, t) for the BCn-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 rational q-difference equation. As s → ∞ the polynomials P*μ(cursive Greek chi; q, t, s) become P*μ(cursive Greek chi; q, t). We also prove a binomial formula for 6-parametric Koornwinder polynomials.

Original languageEnglish
Pages (from-to)181-207
Number of pages27
JournalTransformation Groups
Volume3
Issue number2
DOIs
Publication statusPublished - 1998
Externally publishedYes

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