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

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

1997-10-29

arxiv.org/abs/q-alg/9710036v2

Mathematics

Quantum Algebra

LaTeX2e, 20 pages, minor changes to references

Scientific paper

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 $E_{\eta}(x;q^{-1},t^{-1})$ onto $E_{\eta}(x;q,t)$, while the other maps them onto non-symmetric analogues of the multivariable Al-Salam & Carlitz polynomials. Using the properties of $E_{\eta}(x;q^{-1},t^{-1})$, the corresponding properties of these latter polynomials can then be elucidated.

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