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

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

2003-05-14

arxiv.org/abs/math/0305195v1

Mathematics

Quantum Algebra

LaTeX, 23 pages, no figure

Scientific paper

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.

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