Isomorphisms of type $A$ affine Hecke algebras and multivariable orthogonal polynomials

T. H. Baker; P. J. Forrester

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arXiv · q-alg/9710036

Isomorphisms of type $A$ affine Hecke algebras and multivariable orthogonal polynomials

T. H. Baker·P. J. Forrester

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Abstract

We examine two isomorphisms between affine Hecke algebras of type $A$ associated with parameters $q^{-1}$, $t^{-1}$ and $q$, $t$. One of them maps the non-symmetric Macdonald polynomials $E_η(x;q^{-1},t^{-1})$ onto $E_η(x;q,t)$, while the other maps them onto non-symmetric analogues of the multivariable Al-Salam & Carlitz polynomials. Using the properties of $E_η(x;q^{-1},t^{-1})$, the corresponding properties of these latter polynomials can then be elucidated.

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BibTeX RIS

T. H. Baker, P. J. Forrester. 1997-11-05. Isomorphisms of type $A$ affine Hecke algebras and multivariable orthogonal polynomials. https://arxiv.org/abs/q-alg/9710036

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