Koornwinder polynomials and affine Hecke algebras

Details Koornwinder polynomials and affine Hecke algebras Koornwinder polynomials and affine Hecke algebras

2000-02-11

arxiv.org/abs/math/0002090v2

Internat. Math. Res. Notices 2000, no. 19, 1006-1042

Mathematics

Quantum Algebra

30 pages. Published version, with correction of a mistake in Theorem 3.4 (observed by Etingof, Gan and Oblomkov in math.QA/050

Scientific paper

In this paper we derive the bi-orthogonality relations, diagonal term evaluations and evaluation formulas for the non-symmetric Koornwinder polynomials. For the derivation we use certain representations of the (double) affine Hecke algebra which were originally defined by Noumi and Sahi. The structure of the diagonal terms is clarified by expressing them as residues of the bi-orthogonality weight function. We furthermore give the explicit connection between the non-symmetric and the (anti-)symmetric theory.

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