Jacobson generators of the quantum superalgebra Uq[sl(n+1|m)] and Fock representations

@article{Palev2001JacobsonGO,
  title={Jacobson generators of the quantum superalgebra Uq[sl(n+1|m)] and Fock representations},
  author={Tchavdar D. Palev and N I Stoilova and Joris Van der Jeugt},
  journal={Journal of Mathematical Physics},
  year={2001},
  volume={43},
  pages={1646-1663}
}
As an alternative to Chevalley generators, we introduce Jacobson generators for the quantum superalgebra Uq[sl(n+1|m)]. The expressions of all Cartan–Weyl elements of Uq[sl(n+1|m)] in terms of these Jacobson generators become very simple. We determine and prove certain triple relations between the Jacobson generators, necessary for a complete set of supercommutation relations between the Cartan–Weyl elements. Fock representations are defined, and a substantial part of this paper is devoted to… 
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Jacobson generators of (quantum) sl(n+1|m). Related statistics.

T.D. PALEV †, N.I. STOILOVA ‡ and J. VAN der JEUGT § † Institute for Nuclear Research and Nuclear Energy, Boul. Tsarigradsko Chaussee 72, 1784 Sofia, Bulgaria E-mail: tpalev@inrne.bas.bg ‡

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