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

2003/12/17 by Masahiro Kasatani, Kasatani, Masahiro · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical functions and polynomials #Quantum Algebra (math.QA) #math.CO #math.QA

paper · pdf · doi:10.48550/arxiv.math/0312327

15 pages, self-duality condition is not necessary, so it is removed

openalex publication_date 2003/12/17 · arxiv created 2004/05/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Laurent polynomial solutions of the boundary quantum\n Knizhnik--Zamolodchikov equation

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
• The m-symmetric Macdonald polynomials
• Specializing Koornwinder polynomials to Macdonald polynomials of type B,C,D and B C