Two-parametric deformation $U_{p,q}[gl(2/1)]$ and its induced representations

Abstract

The two-parametric quantum superalgebra $U_{p,q}[gl(2/1)]$ is consistently defined. A construction procedure for induced representations of $U_{p,q}[gl(2/1)]$ is described and allows us to construct explicitly all (typical and nontypical) finite-dimensional representations of this quantum superalgebra. In spite of some specific features, the present approach is similar to a previously developed method [1] which, as shown here, is applicable not only to the one-parametric quantum deformations but also to the multi-parametric ones.

Latex, 13 pages, no figure

Cited by in corpus (2)

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