Double quantization of CPn type orbits by generalized Verma modules

J. Donin, D. Gurevich, S. Khoroshkin

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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 languageEnglish
Pages (from-to)384-406
Number of pages23
JournalJournal of Geometry and Physics
Volume28
Issue number3-4
DOIs
StatePublished - 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.

FundersFunder number
Russian Foundation for Basic Research96-01-01421, 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

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