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Macdonald Polynomials and Algebraic Integrability

✍ Scribed by Oleg A. Chalykh

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 380 KB
Volume: 166
Category: Article
ISSN: 0001-8708
DOI: 10.1006/aima.2001.2033

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✦ Synopsis

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=q k (k ¥ Z), generalizing the result of Etingof and Styrkas. Our approach works uniformly for all root systems including the BC n case and related Koornwinder polynomials. Moreover, we apply it for a certain deformation of the A n root system where the previously known methods do not work.

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