Multivariable Wilson polynomials and degenerate Hecke algebras
Wolter Groenevelt
TL;DR
This paper introduces nonsymmetric multivariable Wilson polynomials derived from a rational double affine Hecke algebra, establishing their orthogonality and norm properties through degenerate Hecke algebra techniques.
Contribution
It presents a novel representation of Wilson polynomials via difference-reflection operators linked to a rational double affine Hecke algebra.
Findings
Orthogonality relations established for Wilson polynomials
Quadratic norms derived for symmetric and nonsymmetric cases
Connection to degenerate Hecke algebra elucidated
Abstract
We study a rational version of the double affine Hecke algebra associated to the nonreduced affine root system of type . A certain representation in terms of difference-reflection operators naturally leads to the definition of nonsymmetric versions of the multivariable Wilson polynomials. Using the degenerate Hecke algebra we derive several properties, such as orthogonality relations and quadratic norms, for the nonsymmetric and symmetric multivariable Wilson polynomials.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics