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1 results

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

  • Masahiro Kasatani
  • Journal:
    Compositio Mathematica / Volume 141 / Issue 6 / November 2005
    Published online by Cambridge University Press:
    04 December 2007, pp. 1589-1601
    Print publication:
    November 2005
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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.