2134/312
A.N. Sergeev
A.N.
Sergeev
Alexander Veselov
Alexander
Veselov
Deformed quantum Calogero-Moser problems and Lie superalgebras
Loughborough University
2005
untagged
Quantum Mechanics
Mathematical Sciences not elsewhere classified
2005-08-01 13:37:09
Preprint
https://repository.lboro.ac.uk/articles/preprint/Deformed_quantum_Calogero-Moser_problems_and_Lie_superalgebras/9383675
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.