Isomorphisms of type A affine Hecke algebras and multivariable orthogonal polynomials

1997/10/29 by T. H. Baker, Peter J. Forrester, Baker, T. H. +2
Chemistry · Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Molecular spectroscopy and chirality #Quantum Algebra (math.QA) #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9710036

LaTeX2e, 20 pages, minor changes to references

openalex publication_date 1997/10/29 · arxiv created 1997/11/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A reproducing kernel for nonsymmetric Macdonald polynomials

Related

• Isomorphisms between affine Hecke algebras
• The Classification of All Singular Nonsymmetric Macdonald Polynomials
• The polynomial representation of the double affine Hecke algebra of type (C^\vee_n, C_n) for specialized parameters
• Automorphisms of the DAHA of type \checkC₁C₁ and non-symmetric Askey-Wilson functions
• Macdonald-Koornwinder polynomials