Finite-dimensional representations of Uq[gl(2/1)] in a basis of Uq[gl(2) gl(1)]
Abstract
The quantum superalgebra Uq[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 Uq[gl(2) 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.
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