A description of the quantum superalgebra $U_q[sl(n+1|m)]$ via creation and annihilation generators

Abstract

A description of the quantum superalgebra $U_q[sl(n+1|m)]$ and in particular of the special linear superalgebra $sl(n+1|m)$ via creation and annihilation generators (CAGs) is given. It provides an alternative to the canonical description of $U_q[sl(n+1|m)]$ in terms of Chevalley generators. A conjecture that the Fock representations of the CAGs provide microscopic realizations of exclusion statistics is formulated.

16 pages, TeX; an extended version of a paper to appear in J. Phys. A; a multiple in the RHS of Eq. (38d) was added

References in corpus (3)

• Lie Algebraical Aspects of the Quantum Statistics. Unitary Quantization (A-quantization)
• A q-deformation of the parastatistics and an alternative to the Chevalley description of $U_q[osp(2n+1/2m)]$
• Unification of parastatistics defined as triple operator algebras

Cited by in corpus (5)

• Low-Energy Effective Action of N=2 Gauge Multiplet Induced by Hypermultiplet Matter
• Fock representations of the superalgebra sl(n+1|m), its quantum analogue U_q[sl(n+1|m)] and related quantum statistics
• Weyl-Wigner-Moyal formulation of a Dirac quantized constrained system
• A Dyson realization and a Holstein-Primakoff realization for the quantum superalgebra $U_q[gl(n/m)]$
• Jacobson generators of the quantum superalgebra $U_q[sl(n+1|m)]$ and Fock representations