2004/06/09 by Gail Letzter, Letzter, Gail
Mathematics · #17B37 #Advanced Algebra and Geometry #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B37
paper · pdf · doi:10.48550/arxiv.math/0406194
arxiv created 2004/06/09 · openalex publication_date 2004/06/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The two papers in this series analyze quantum invariant differential operators for quantum symmetric spaces in the maximally split case. In this paper, we complete the proof of a quantum version of Harish-Chandra's theorem: There is a Harish-Chandra map which induces an isomorphism between the ring of quantum invariant differential operators and a ring of Laurent polynomial invariants with respect to the dotted action of the restricted Weyl group. We find a particularly nice basis for the quantum invariant differential operators that provides a new interpretation of difference operators associated to Macdonald polynomials. Finally, we set the stage for a general quantum counterpart to noncompact zonal spherical functions.