dorsal/arxiv
View SchemaOn Quantum Orbit Method
| Authors | Leonid I. Korogodsky |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9708026 |
| URL | https://arxiv.org/abs/q-alg/9708026 |
Abstract
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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"abstract": "A version of quantum orbit method is presented for real forms of equal rank\nof quantum complex simple groups. A quantum moment map is constructed, based on\nthe canonical isomorphism between a quantum Heisenberg algebra and an algebra\nof functions on a family of quantum G-spaces. For the series $A$, we construct\nsome irreducible $*$-representations of $U_q{\\frak g}$ which correspond to the\nsemi-simple dressing orbits of minimal dimension in the dual Poisson Lie group.\nIt is shown that some complimentary series representations correspond to some\nquantum \u0027tunnel\u0027 G-spaces which do not have a quasi-classical analog.",
"arxiv_id": "q-alg/9708026",
"authors": [
"Leonid I. Korogodsky"
],
"categories": [
"q-alg",
"math.QA"
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"title": "On Quantum Orbit Method",
"url": "https://arxiv.org/abs/q-alg/9708026"
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