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

The quantum superalgebra $U_q[gl(2\mathrm{/}1)]$ is given as both a Drinfel’d–Jimbo deformation of $U[gl(2\mathrm{/}1)]$ 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.