Multivariable Wilson polynomials and degenerate Hecke algebras

Details Multivariable Wilson polynomials and degenerate Hecke algebras Multivariable Wilson polynomials and degenerate Hecke algebras

2007-10-16

arxiv.org/abs/0710.3078v1

Selecta Math. (N.S.) 15 (2009), no. 3, 377-418

Mathematics

Representation Theory

30 pages

Scientific paper

We study a rational version of the double affine Hecke algebra associated to the nonreduced affine root system of type $(C^\vee_n,C_n)$. 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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