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We construct a Bernstein-Gelfand-Gelfand type resolution in terms of directsums of Kac modules for the finite-dimensional irreducible tensorrepresentations of the general linear superalgebra. As a consequence it followsthat the unique maximal submodule of a corresponding reducible Kac module isgenerated by its proper singular vector.

A BGG-type resolution for tensor modules over general linear superalgebra