Abstract. It is shown how to associate to a highest weight Λ of the Lie superalgebra gl(m|n) a composite partition ‾ν;μ with composite Young diagram F(‾ν;μ). The corresponding supersymmetric Schur function s_‾ν;μ(x/y) is defined. However, it is known that this S-function does not always coincide with the character of the irreducible representation V _Λ with highest weight Λ. Only for covariant, contravariant and typical representations the character and the S-function are known to coincide.
Here, the notions of critical composite partitions and critical highest weights are considered. It is shown that for critical composite partitions (subject to a technical restriction) the corresponding gl(m|n) representation V_Λ is tame, so its character can be computed. Also for this class of representations the character coincides with the composite supersymmetric S-function s_‾ν;μ(x/y). This extends considerably the classes of gl(m|n) representations for which the character can be computed by means of S-functions.

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