2000
DOI: 10.2140/pjm.2000.194.19
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Isomorphisms of type A affine Hecke algebras and multivariable orthogonal polynomials

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 nonsymmetric 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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Cited by 4 publications
(2 citation statements)
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“…The Cherednik operators, denoted by Y i , are defined in terms of Dunkl operators and have important applications in representation theory [2,20]. They have non-degenerate simultaneous eigenfunctions, known as Jack polynomials.…”
Section: The Commutative ("Even") Casementioning
confidence: 99%
See 1 more Smart Citation
“…The Cherednik operators, denoted by Y i , are defined in terms of Dunkl operators and have important applications in representation theory [2,20]. They have non-degenerate simultaneous eigenfunctions, known as Jack polynomials.…”
Section: The Commutative ("Even") Casementioning
confidence: 99%
“…We also need to investigate what the third commutativity relation [r 2 , ∆] turns out to be. We will prove one lemma before doing so.…”
Section: A Variant Of the Khongsap-wang Odd Dunkl Operatormentioning
confidence: 99%