Nonsymmetric Koornwinder Polynomials and Duality
Copyright policy )Nonsymmetric Koornwinder Polynomials and Duality
Motivated by the work of Koornwinder, Macdonald, Cherednik, Noumi, and van Diejen we define a 6-parameter double affine Hecke algebra and establish its basic structural properties, including the existence of an involution. We relate the algebra to (symmetric and nonsymmetric) Koornwinder polynomials via the method of intertwiners and, as a consequence, obtain a proof of Macdonald's duality conjecture for Koornwinder polynomials. Combined with earlier work of van Diejen this completely settles all the outstanding conjectures of Macdonald and Koornwinder about these polynomials.
16 pages, published version
affine Hecke algebra, Askey-Wilson polynomials, duality conjecture, Combinatorial aspects of groups and algebras, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Macdonald polynomials, double affine Hecke algebra, Orthogonal polynomials (combinatorics), Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, Simple, semisimple, reductive (super)algebras, Koornwinder polynomials
affine Hecke algebra, Askey-Wilson polynomials, duality conjecture, Combinatorial aspects of groups and algebras, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Macdonald polynomials, double affine Hecke algebra, Orthogonal polynomials (combinatorics), Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, Simple, semisimple, reductive (super)algebras, Koornwinder polynomials
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