Boson-fermion realisation of indecomposable representations for Lie superalgebras

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Abstract
Indecomposable representations of Lie superalgebras are studied on quotient spaces of the universal enveloping algebra of the Heisenberg-Weyl superalgebra (b+i,bi,f+u,e) by boson-fermion realisation. These representations are constructed from certain types of indecomposable representations of the Heisenberg-Weyl superalgebra and induce usual irreducible representations on invariant subspaces of a quotient space. As a physically significant example, the explicit form of the boson-fermion realisation of indecomposable representations of the classical Lie superalgebra SU(2/1) are obtained and discussed.