The non-symmetric Wilson polynomials are the Bannai-Ito polynomials (Q2827371)
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scientific article; zbMATH DE number 6640944
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The non-symmetric Wilson polynomials are the Bannai-Ito polynomials |
scientific article; zbMATH DE number 6640944 |
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19 October 2016
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non-symmetric Wilson polynomials
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Bannai-Ito polynomials
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double affine Hecke algebras
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Bannai-Ito algebras
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The non-symmetric Wilson polynomials are the Bannai-Ito polynomials (English)
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In this paper, the authors identify the one-variable non-symmetric Wilson polynomials with the Bannai-Ito polynomials, and identify the corresponding degenerate double affine Hecke algebra of type \((C_1^\vee ;C_1)\) with the Bannai-Ito algebra by constructing an isomorphism. They also present a positive-definite and continuous measure on the real line for the Bannai-Ito polynomials, a non-compact form of the Bannai-Ito algebra, as well as a four-parameter family of its infinite-dimensional and self-adjoint representations.
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