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Invariant differential operators for quantum symmetric spaces, II

Gail Letzter
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Abstract

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.

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Gail Letzter. 2004-06-09. Invariant differential operators for quantum symmetric spaces, II. https://arxiv.org/abs/math/0406194

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