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

2005/11/01 by Masahiro Kasatani
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Nonlinear Waves and Solitons #Algebraic structures and combinatorial models

paper · pdf · doi:10.1112/s0010437x05001570

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.

Related

• Zeros of Symmetric Laurent Polynomials of Type (BC)_n and Koornwinder-Macdonald Polynomials Specialized at t^k+1q^r-1=1
• BC_n-symmetric polynomials
• Symmetric polynomials vanishing on the diagonals shifted by roots of unity
• Specializing Koornwinder polynomials to Macdonald polynomials of type B,C,D and B C
• Quadratic transformations of Macdonald and Koornwinder polynomials