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We derive a closed formula for the tensor product of a family of mixed tensors using Deligne’s interpolating category $\underline {Rep}(GL_{0})$. We use this formula to compute the tensor product of a family of irreducible GL(n|n)-representations. This includes the tensor product of any two maximal atypical irreducible representations of GL(2|2).

Pieri Type Rules and GL(2|2) Tensor Products