Self-dual Koornwinder-Macdonald polynomials

1995/07/31 by J. F. van Diejen, Jan F. van Diejen · 5 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.CA #math.QA #q-alg

paper · pdf · doi:10.1007/s002220050102

published as Invent. Math. 126 (1996), 319--339 · 21 pages, AMSLaTeX 1.1 with amssymb

arxiv created 1995/07/31 · openalex publication_date 1996/10/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove certain duality properties and present recurrence relations for a four-parameter family of self-dual Koornwinder-Macdonald polynomials. The recurrence relations are used to verify Macdonald's normalization conjectures for these polynomials.

Citations

• Representation-theoretic proof of the inner product and symmetry identities for MacDonald's polynomials
• Quantum symmetric spaces and related q-orthogonal polynomials
• On the diagonalization of difference Calogero-Sutherland systems

Cited by

• Properties of some families of hypergeometric orthogonal polynomials in several variables
• Multivariable q-Racah polynomials
• The importance of the Selberg integral
• Nonsymmetric Koornwinder Polynomials and Duality
• Koornwinder polynomials [wikipedia]