Invariant Differential Operators for Quantum Symmetric Spaces, II
نویسنده
چکیده
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.
منابع مشابه
un 2 00 4 Invariant Differential Operators for Quantum Symmetric Spaces
This is the first paper in a series of two which proves a version of a theorem of Harish-Chandra for quantum symmetric spaces in the maximally split case: 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. Here, we est...
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