Invariant Differential Operators For Quantum Symmetric Spaces
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Invariant Differential Operators for Quantum Symmetric Spaces
This paper studies quantum invariant differential operators for quantum symmetric spaces in the maximally split case. The main results are quantum versions of theorems of Harish-Chandra and Helgason: There is a Harish-Chandra map which induces an isomorphism between the ring of quantum invariant differential operators and the ring of invariants of a certain Laurent polynomial ring under an action of the restricted Weyl group. Moreover, the image of the center under this map is the entire invariant ring if and only if the underlying irreducible symmetric pair is not of four exceptional types. In the process, the author finds a particularly nice basis for the quantum invariant differential operators that provides a new interpretation of difference operators associated to Macdonald polynomials.
Invariant Differential Operators for Quantum Symmetric Spaces
Studies quantum invariant differential operators for quantum symmetric spaces in the maximally split case. The author finds a fresh basis for the quantum invariant differential operators that provides a new interpretation of difference operators associated to Macdonald polynomials.
Classical And Quantum Systems: Foundations And Symmetries - Proceedings Of The 2nd International Wigner Symposium
Author: Heinz-dietrich Doebner
language: en
Publisher: World Scientific
Release Date: 1993-01-19
The Wigner Symposium series is focussed on fundamental problems and new developments in physics and their experimental, theoretical and mathematical aspects. Particular emphasis is given to those topics which have developed from the work of Eugene P Wigner. The 2nd Wigner symposium is centered around notions of symmetry and geometry, the foundations of quantum mechanics, quantum optics and particle physics. Other fields like dynamical systems, neural networks and physics of information are also represented.This volume brings together 19 plenary lectures which survey latest developments and more than 130 contributed research reports.