Finite-dimensional representations of U_q[gl(2/1)] in a basis of U_q[gl(2)\oplus gl(1)]

Abstract

The quantum superalgebra $U_q[gl(2/1)]$ is given as both a Drinfel'd--Jimbo deformation of $U[gl(2/1)]$ and a Hopf superalgebra. Finite--dimensional representations of this quantum superalgebra are constructed and investigated in a basis of its even subalgebra $U_q[gl(2)\oplus gl(1)]$. The present method for constructing representations of a quantum superalgebra combines previously suggested ones for the cases of superalgebras and quantum superalgebras, and, therefore, has an advantage in comparison with the latter.

arXiv commentLaTeX, 23 pages, no figure

References in corpus (1)

• Superalgebras, their quantum deformations and the induced representation method

Cited by in corpus (1)

• Baxter's Q-operators for supersymmetric spin chains