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Zeros of symmetric Laurent polynomials of type (BC)n and Koornwinder–Macdonald polynomials specialized at $t^{k+1}q^{r-1}=1$

Published online by Cambridge University Press:  04 December 2007

Masahiro Kasatani
Masahiro Kasatani
Affiliation:
Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japankasatani@math.kyoto-u.ac.jp
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Abstract

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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.

Keywords

symmetric polynomialsKoornwinder–Macdonald polynomialsdouble affine Hecke algebra33D52 (primary)05E05 (secondary)

Information

Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 6 , November 2005 , pp. 1589 - 1601
Copyright
Foundation Compositio Mathematica 2005