Finite Dimensional Representations of the Quantum Superalgebra $U_q[gl(3/2)]$ in a Reduced $U_q[gl(3/2)]\supset U_q[gl(3/1)]\supset U_q[gl(3)]$ Basis

Abstract

For generic $q$ we give expressions for the transformations of all essentially typical finite-dimensional modules of the Hopf superalgebra $U_q[gl(3/2)]$. The latter is a deformation of the universal enveloping algebra of the Lie superalgebra $gl(3/2)$. The basis within each module is similar to the Gel'fand-Zetlin basis for $gl(5)$. We write down expressions for the transformations of the basis under the action of the Chevalley generators.

7 pages, emTeX, University of Ghent Int. Report TWI-93-21

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