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arXiv · 1406.0444

Mixed Tensors of the General Linear Supergroup

Thorsten Heidersdorf
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Abstract

We describe the image of the canonical tensor functor from Deligne's interpolating category $Rep(GL_{m-n})$ to $Rep(GL(m|n))$ attached to the standard representation. This implies explicit tensor product decompositions between any two projective modules and any two Kostant modules of $GL(m|n)$, covering the decomposition between any two irreducible $GL(m|1)$-representations. We also obtain character and dimension formulas. For $m>n$ we classify the mixed tensors with non-vanishing superdimension. For $m=n$ we characterize the maximally atypical mixed tensors and show some applications regarding tensor products.

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BibTeXRIS

Thorsten Heidersdorf. 2014-06-02. Mixed Tensors of the General Linear Supergroup. https://arxiv.org/abs/1406.0444

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