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Vanishing Integrals of Macdonald and Koornwinder polynomials

✍ Scribed by Eric M. Rains; Monica Vazirani

Publisher
SP Birkhäuser Verlag Boston
Year
2007
Tongue
English
Weight
339 KB
Volume
12
Category
Article
ISSN
1083-4362

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We construct explicitly (nonpolynomial) eigenfunctions of the difference operators by Macdonald in the case t=q k , k ¥ Z. This leads to a new, more elementary proof of several Macdonald conjectures, proved first by Cherednik. We also establish the algebraic integrability of Macdonald operators at t

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Dunkl operators are differential-difference operators on R N which generalize partial derivatives. They lead to generalizations of Laplace operators, Fourier transforms, heat semigroups, Hermite polynomials, and so on. In this paper we introduce two systems of biorthogonal polynomials with respect t