Let g=g0ˉ​⊕g1ˉ​ be a
classical Lie superalgebra and F be the category of finite
dimensional g-supermodules which are completely reducible over the
reductive Lie algebra g0ˉ​. In an earlier paper the authors
demonstrated that for any module M in F the rate of growth of the
minimal projective resolution (i.e., the complexity of M) is bounded by the
dimension of g1ˉ​. In this paper we compute the complexity
of the simple modules and the Kac modules for the Lie superalgebra
gl(m∣n). In both cases we show that the complexity is related to
the atypicality of the block containing the module.Comment: 32 page