Isomorphisms of type A affine Hecke algebras and multivariable orthogonal polynomials

Citation
Th. Baker et Pj. Forrester, Isomorphisms of type A affine Hecke algebras and multivariable orthogonal polynomials, PAC J MATH, 194(1), 2000, pp. 19-41
Citations number
29
Categorie Soggetti
Mathematics
Journal title
PACIFIC JOURNAL OF MATHEMATICS
ISSN journal
00308730 → ACNP
Volume
194
Issue
1
Year of publication
2000
Pages
19 - 41
Database
ISI
SICI code
0030-8730(200005)194:1<19:IOTAAH>2.0.ZU;2-B
Abstract
We examine two isomorphisms between affine Hecke algebras of type A associa ted with parameters q(-1), t(-1) and q, t. One of them maps the non-symmetr ic 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-Sa lam & Carlitz polynomials. Using the properties of E-eta(x; q(-1), t(-1)), the corresponding properties of these latter polynomials can then be elucid ated.