dorsal/arxiv
View SchemaIsomorphisms of type $A$ affine Hecke algebras and multivariable orthogonal polynomials
| Authors | T. H. Baker, P. J. Forrester |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9710036 |
| URL | https://arxiv.org/abs/q-alg/9710036 |
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 $E_{\eta}(x;q^{-1},t^{-1})$ 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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"abstract": "We examine two isomorphisms between affine Hecke algebras of type $A$\nassociated with parameters $q^{-1}$, $t^{-1}$ and $q$, $t$. One of them maps\nthe non-symmetric Macdonald polynomials $E_{\\eta}(x;q^{-1},t^{-1})$ onto\n$E_{\\eta}(x;q,t)$, while the other maps them onto non-symmetric analogues of\nthe multivariable Al-Salam \u0026 Carlitz polynomials. Using the properties of\n$E_{\\eta}(x;q^{-1},t^{-1})$, the corresponding properties of these latter\npolynomials can then be elucidated.",
"arxiv_id": "q-alg/9710036",
"authors": [
"T. H. Baker",
"P. J. Forrester"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Isomorphisms of type $A$ affine Hecke algebras and multivariable orthogonal polynomials",
"url": "https://arxiv.org/abs/q-alg/9710036"
},
"schema_id": "dorsal/arxiv",
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"variant": "snapshot-2026-03-01",
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