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Journal of Mathematical Physics 52, 123512 (2011)


Representations of quantum superalgebra U_q[ gl(2|1)] in a coherent state basis and generalization

Nguyen Cong Kien, Nguyen Anh Ky, Le Ba Nam, and Nguyen Thi Hong Van

The coherent statemethod has proved to be useful in quantum physics and mathematics. This method, more precisely, the vector coherent state method, has been used by some authors to construct representations of superalgebras but almost, to our knowledge, it has not yet been extended to quantum superalgebras, except Uq[osp(1|2)], one of the smallest quantum superalgebras. In this article the method is applied to a bigger quantum superalgebra, namely Uq[gl(2|1)], in constructing q–boson-fermion realizations and finite-dimensional representations which, when irreducible, are classified into typical and nontypical representations. This construction leads to a more general class of q–boson-fermion realizations and finite-dimensional representations of Uq[gl(2|1)] and, thus, at q = 1, of gl(2|1). Both gl(2|1) and Uq[gl(2|1)] have found different physics applications, therefore, it is meaningful to construct their representations