Deformed Quantum Calogero-Moser Problems and Lie Superalgebras |
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Authors: | Sergeev AN Veselov AP |
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Institution: | (1) Balakovo Institute of Technology and Control, 413800 Balakovo, Russia;(2) Department of Mathematical Sciences, Loughborough University, Loughborough, LE11 3TU, UK;(3) Landau Institute for Theoretical Physics, Kosygina 2, 117940 Moscow, Russia |
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Abstract: | 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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