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# Deformed quantum Calogero-Moser problems and Lie superalgebras

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.

## History

## School

- Science

## Department

- Mathematical Sciences

## Pages

285552 bytes## Publication date

2003## Notes

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.## Language

- en