Zeros of Symmetric Laurent Polynomials of Type (BC)n and Koornwinder-Macdonald Polynomials Specialized at tk+1qr-1=1
Abstract
A characterization of the space of symmetric Laurent polynomials of type (BC)n which vanish on a certain set of submanifolds is given by using the Koornwinder-Macdonald polynomials. A similar characterization was given previously for symmetric polynomials of type An by using the Macdonald polynomials. We use a new method which exploits the duality relation. The method simplifies a part of the proof in the An case.
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