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...

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Main Authors: A.N. Sergeev, Alexander Veselov
Format: Default Preprint
Published: 2003
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Online Access:https://hdl.handle.net/2134/312
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spelling rr-article-93836752003-01-01T00:00:00Z Deformed quantum Calogero-Moser problems and Lie superalgebras A.N. Sergeev (7160591) Alexander Veselov (1259028) Other mathematical sciences not elsewhere classified Foundations of quantum mechanics untagged Quantum Mechanics Mathematical Sciences not elsewhere classified 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. 2003-01-01T00:00:00Z Text Preprint 2134/312 https://figshare.com/articles/preprint/Deformed_quantum_Calogero-Moser_problems_and_Lie_superalgebras/9383675 CC BY-NC-ND 4.0
institution Loughborough University
collection Figshare
topic Other mathematical sciences not elsewhere classified
Foundations of quantum mechanics
untagged
Quantum Mechanics
Mathematical Sciences not elsewhere classified
spellingShingle Other mathematical sciences not elsewhere classified
Foundations of quantum mechanics
untagged
Quantum Mechanics
Mathematical Sciences not elsewhere classified
A.N. Sergeev
Alexander Veselov
Deformed quantum Calogero-Moser problems and Lie superalgebras
description 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.
format Default
Preprint
author A.N. Sergeev
Alexander Veselov
author_facet A.N. Sergeev
Alexander Veselov
author_sort A.N. Sergeev (7160591)
title Deformed quantum Calogero-Moser problems and Lie superalgebras
title_short Deformed quantum Calogero-Moser problems and Lie superalgebras
title_full Deformed quantum Calogero-Moser problems and Lie superalgebras
title_fullStr Deformed quantum Calogero-Moser problems and Lie superalgebras
title_full_unstemmed Deformed quantum Calogero-Moser problems and Lie superalgebras
title_sort deformed quantum calogero-moser problems and lie superalgebras
publishDate 2003
url https://hdl.handle.net/2134/312
_version_ 1802814942258135040