A q-deformation of the parastatistics and an alternative to the Chevalley description of $U_q[osp(2n+1/2m)]$

Abstract

The paper contains essentially two new results. Physically, a deformation of the parastatistics in a sense of quantum groups is carried out. Mathematically, an alternative to the Chevalley description of the quantum orthosymplectic superalgebra U_q[osp(2n+1/2m)] in terms of $m$ pairs of deformed parabosons and $n$ pairs of deformed parafermions is outlined.

14 pages, TeX, minor misprints corrected. To be published in Comm. Math. Phys

References in corpus (1)

• Lie Algebraical Aspects of the Quantum Statistics. Unitary Quantization (A-quantization)

Cited by in corpus (9)

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• Parastatistics Algebra, Young Tableaux and the Super Plactic Monoid
• Fock representations of the superalgebra sl(n+1|m), its quantum analogue U_q[sl(n+1|m)] and related quantum statistics
• A description of the quantum superalgebra $U_q[sl(n+1|m)]$ via creation and annihilation generators
• Deformed Clifford Cl_q(n|m) and orthosymplectic U_q[osp(2n+1|2m)] superalgebras and their root of unity representations
• Parastatistics Algebra and Super Semistandard Young Tableaux
• Jacobson generators of the quantum superalgebra $U_q[sl(n+1|m)]$ and Fock representations
• Highest weight irreducible representations of the Lie superalgebra $gl(1/\infty )$