Abstract
It is known that symmetric orbits in g* for any simple Lie algebra g are equipped with a Poisson pencil generated by the Kirillov-Kostant-Souriau bracket and the reduced Sklyanin bracket associated to the "canonical" R-matrix. We realize quantization of the Poisson pencil on CPn type orbits (i.e. orbits in sl(n + 1)* whose real compact form is CPn) by means of q-deformed Verma modules.
Original language | English |
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Pages (from-to) | 384-406 |
Number of pages | 23 |
Journal | Journal of Geometry and Physics |
Volume | 28 |
Issue number | 3-4 |
DOIs | |
State | Published - Dec 1998 |
Bibliographical note
Funding Information:The authors are deeply indebted to S. Majid and N. Zobin who read a preliminary version of the paper and made valuable remarks. One of the authors (SK) was supported by the grants RFBR 96-01-01421 and INTAS 93-10183. He would also like to thank Universitt Lille-1 (France) for the warm hospitality during his stay when this paper was started.
Funding
The authors are deeply indebted to S. Majid and N. Zobin who read a preliminary version of the paper and made valuable remarks. One of the authors (SK) was supported by the grants RFBR 96-01-01421 and INTAS 93-10183. He would also like to thank Universitt Lille-1 (France) for the warm hospitality during his stay when this paper was started.
Funders | Funder number |
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Russian Foundation for Basic Research | 96-01-01421, INTAS 93-10183 |
Keywords
- (Double) quantization
- (Generalized) verma module
- (Twisted) hopf algebra
- Braided algebra
- Braided module
- Flat deformation
- Orbit of CP type
- Poisson bracket
- Poisson pencil
- Quantum group
- R-matrix bracket