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Deformed quantum Calogero-Moser problems and Lie superalgebras

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preprint
posted on 01.08.2005, 13:37 by A.N. Sergeev, Alexander VeselovAlexander Veselov
The deformed quantum Calogero-Moser-Sutherland problems related to the root systems of the contragredient Lie superalgebras are introduced. The construction is based on the notion of the generalized root systems suggested by V. Serganova. For the classical series a recurrent formula for the quantum integrals is found, which implies the integrability of these problems. The corresponding algebras of the quantum integrals are investigated, the explicit formulas for their Poincare series for generic values of the deformation parameter are presented.

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  • Science

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  • Mathematical Sciences

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285552 bytes

Publication date

2003

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This pre-print has been submitted, and accepted, to the journal, Communications in Mathematical Physics [© Springer].The definitive version: SERGEEV, A.N. and VESELOV, A.P., 2004. Deformed quantum Calogero-Moser problems and Lie superalgebras. Communications in Mathematical Physics, 245(2), pp. 249-278, is available at: http://www.springerlink.com/openurl.asp?genre=journal&eissn=1432-0916.

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