Nonsymmetric interpolation Macdonald polynomials and \({\mathfrak {gl}}_n\) basic hypergeometric series

DOI10.1007/s00031-009-9061-1zbMath1179.33027arXiv0807.1351OpenAlexW1513154940MaRDI QIDQ733678

Eric M. Rains, S. Ole Warnaar, Lascoux, Alain

Publication date: 19 October 2009

Published in: Transformation Groups (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.1351

zbMATH Keywords

\(q\)-Gauss sumstransformation formulae

Mathematics Subject Classification ID

Basic orthogonal polynomials and functions associated with root systems (Macdonald polynomials, etc.) (33D52) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items

Notes on Schubert, Grothendieck and key polynomials ⋮ Nonterminating q-Whipple Transformations for Basic Hypergeometric Series in U(n) ⋮ Remarks on the paper ``skew Pieri rules for Hall-Littlewood functions by Konvalinka and Lauve ⋮ \(p^\ell\)-torsion points in finite abelian groups and combinatorial identities ⋮ Branching rules for symmetric functions and \(\mathfrak{sl}_n\) basic hypergeometric series ⋮ Bounded Littlewood identities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Elliptic Littlewood identities
• \(BC_n\)-symmetric abelian functions
• A q-analog of the \(_5F_4(1)\) summation theorem for hypergeometric series well-poised in \(SU(n)\)
• An elementary proof of the Macdonald identities for \(A_{\ell}^{(1)}\)
• \(BC\)-type interpolation Macdonald polynomials and binomial formula for Koornwinder polynomials
• Generalized binomial coefficients and Macdonald polynomials
• On Newton interpolation of symmetric functions: A characterization of interpolation Macdonald polynomials
• Symmetric and non-symmetric quantum Capelli polynomials
• Binomial formula for Macdonald polynomials and applications
• Transformation formulas for multivariable basic hypergeometric series
• Isomorphisms of type \(A\) affine Hecke algebras and multivariable orthogonal polynomials
• Yang-Baxter graphs, Jack and Macdonald polynomials
• The binomial formula for nonsymmetric Macdonald polynomials
• BC\(_n\)-symmetric polynomials
• Affine Hecke Algebras and Their Graded Version
• Multilateral Summation Theorems for Ordinary and Basic Hypergeometric Series in $U(n)$.
• $q$-Selberg integrals and Macdonald polynomials
• Integrality of two variable Kostka functions.
• A new class of symmetric functions