2002/10/29 by Gail Letzter, Letzter, Gail
Mathematics · #17B37 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Mathematical functions and polynomials #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B37
paper · pdf · doi:10.48550/arxiv.math/0210447
Minor revisions, changes to section 7
openalex publication_date 2002/10/29 · arxiv created 2003/02/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A unified theory of quantum symmetric pairs is applied to q-special functions. Previous work characterized certain left coideal subalgebras in the quantized enveloping algebra and established an appropriate framework for quantum zonal spherical functions. Here a distinguished family of such functions, invariant under the Weyl group associated to the restricted roots, is shown to be a family of Macdonald polynomials, as conjectured by Koornwinder and Macdonald. Our results place earlier work for Lie algebras of classical type in a general context and extend to the exceptional cases.