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Zeros of Symmetric Laurent Polynomials of Type $(BC)_n$ and Koornwinder-Macdonald Polynomials Specialized at $t^{k+1}q^{r-1}=1$

Masahiro Kasatani
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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 $A_n$ 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 $A_n$ case.

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Masahiro Kasatani. 2004-05-11. Zeros of Symmetric Laurent Polynomials of Type $(BC)_n$ and Koornwinder-Macdonald Polynomials Specialized at $t^{k+1}q^{r-1}=1$. https://arxiv.org/abs/math/0312327

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