Self-dual Koornwinder-Macdonald polynomials

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.

21 pages, AMSLaTeX 1.1 with amssymb

References in corpus (6)

• Macdonald's Evaluation Conjectures and Difference Fourier Transform
• Commuting difference operators with polynomial eigenfunctions
• Quantum symmetric spaces and related q-orthogonal polynomials
• Representation-theoretic proof of the inner product and symmetry identities for Macdonald's polynomials
• Representation-theoretic proof of the inner product and symmetry identities for MacDonald's polynomials
• On the diagonalization of difference Calogero-Sutherland systems

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• Transformations of elliptic hypergometric integrals
• Multivariable q-Racah polynomials
• Askey-Wilson polynomials: an affine Hecke algebraic approach
• Raising and Lowering Operators for Askey-Wilson Polynomials
• Branching Formula for Macdonald-Koornwinder Polynomials
• Koornwinder polynomials and affine Hecke algebras
• Some results on the eigenfunctions of the quantum trigonometric Calogero-Sutherland model related to the Lie Algebra $D_4$
• BC_n-symmetric polynomials
• Matrix product construction for Koornwinder polynomials and fluctuations of the current in the open ASEP
• S-duality of boundary lines in $\mathcal{N}=4$ SYM theories and supersymmetric indices
• Branching Rules for Symmetric Hypergeometric Polynomials
• Nonsymmetric Koornwinder polynomials and duality
• A determinant formula associated with the elliptic hypergeometric integrals of type $B{C}_n$
• On BC type basic hypergeometric orthogonal polynomials
• A Pieri formula for Macdonald's spherical functions and polynomials
• Difference Fourier transforms for nonreduced root systems
• Memories of Ian G. Macdonald
• BC_n-symmetric abelian functions
• Interface line operators in $\mathcal{N}=4$ SYM theories and supersymmetric indices
• Quantum dimensions and their non-Archimedean degenerations
• Proof of some Littlewood identities conjectured by Lee, Rains and Warnaar
• Generalized Macdonald-Ruijsenaars systems
• Kernel identities for van Diejen's $q$-difference operators and transformation formulas for multiple basic hypergeometric series