Isomorphisms of type A affine Hecke algebras and multivariable orthogonal polynomials
Copyright policy )Isomorphisms of type A affine Hecke algebras and multivariable orthogonal polynomials
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 $E_��(x;q^{-1},t^{-1})$ onto $E_��(x;q,t)$, while the other maps them onto non-symmetric analogues of the multivariable Al-Salam & Carlitz polynomials. Using the properties of $E_��(x;q^{-1},t^{-1})$, the corresponding properties of these latter polynomials can then be elucidated.
LaTeX2e, 20 pages, minor changes to references
- University of Melbourne Australia
Carlitz polynomials, Dunkl operators, Hecke algebra, Al-Salam polynomials, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), non-symmetric Macdonald polynomial, Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Hecke algebras and their representations
Carlitz polynomials, Dunkl operators, Hecke algebra, Al-Salam polynomials, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), non-symmetric Macdonald polynomial, Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics, Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.), Hecke algebras and their representations
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