Induced Representations of the Two Parametric Quantum Deformation U$_{pq}$[gl(2/2)]

Details Induced Representations of the Two Parametric Quantum Deformation U$_{pq}$[gl(2/2)] Induced Representations of the Two Parametric Quantum Deformation U$_{pq}$[gl(2/2)]

2000-05-12

arxiv.org/abs/math/0005122v1

J.Math.Phys. 41 (2000) 6487-6508

Mathematics

Quantum Algebra

Latex, 40 pages, no figure. To appear in J. Math. Phys. 41 (2000)

Scientific paper

The two-parametric quantum superalgebra $U_{p,q}[gl(2/2)]$ and its induced representations are considered. A method for constructing all finite-dimensional irreducible representations of this quantum superalgebra is also described in detail. It turns out that finite-dimensional representations of the two-parametric $U_{p,q}[gl(2/2)]$, even at generic deformation parameters, are not simply trivial deformations from those of the classical superalgebra $gl(2/2)$, unlike the one-parametric cases.

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