On Quantum Orbit Method

Details On Quantum Orbit Method On Quantum Orbit Method

1997-08-22

arxiv.org/abs/q-alg/9708026v1

Mathematics

Quantum Algebra

24 pages, AMS-LaTeX

Scientific paper

A version of quantum orbit method is presented for real forms of equal rank of quantum complex simple groups. A quantum moment map is constructed, based on the canonical isomorphism between a quantum Heisenberg algebra and an algebra of functions on a family of quantum G-spaces. For the series $A$, we construct some irreducible $*$-representations of $U_q{\frak g}$ which correspond to the semi-simple dressing orbits of minimal dimension in the dual Poisson Lie group. It is shown that some complimentary series representations correspond to some quantum 'tunnel' G-spaces which do not have a quasi-classical analog.

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