Deformed quantum Calogero-Moser problems and Lie superalgebras

Details Deformed quantum Calogero-Moser problems and Lie superalgebras Deformed quantum Calogero-Moser problems and Lie superalgebras

2003-03-10

arxiv.org/abs/math-ph/0303025v1

Physics

Mathematical Physics

30 pages, 1 figure

Scientific paper

10.1007/s00220-003-1012-4

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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