Koornwinder Polynomials and Affine Hecke Algebras
نویسنده
چکیده
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. We furthermore give the explicit connection between the non-symmetric and the symmetric theory. This leads in particular to new proofs of the orthogonality relations, quadratic norm evaluations and evaluation formulas for the symmetric Koornwinder polynomials.
منابع مشابه
Nonsymmetric Koornwinder Polynomials and Duality
In the fundamental work of Lusztig [L] on affine Hecke algebras, a special role is played by the root system of type C̃n. The affine Hecke algebra is a deformation of the group algebra of an affine Weyl group which usually depends on as many parameters as there are distinct root lengths, i.e. one or two for an irreducible root system. However in the C̃n case, the Hecke algebra H has three paramet...
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