Fock space representations of the Lie superalgebra A(0,n)

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Abstract
An infinite class of finite-dimensional irreducible representations and one particular infinite-dimensional representation of the special linear superalgebra of an arbitrary rank is constructed. For every representation an orthonormal basis in the corresponding representation space is found, and the matrix elements of the generators are calculated. The method we use is similar to the one applied in quantum theory to compute the Fock space representations of Bose and Fermi operators. For this purpose we first introduce a concept of creation and annihilation operators of a simple Lie superalgebra and give a definition of Fock-space representations.

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