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arXiv · 1406.0321

Cohomological Tensor Functors on Representations of the General Linear Supergroup

Thorsten Heidersdorf·Rainer Weissauer
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Abstract

We define and study cohomological tensor functors from the category $T_n$ of finite-dimensional representations of the supergroup $Gl(n|n)$ into $T_{n-r}$ for $0 <r \leq n$. In the case $DS: T_n \to T_{n-1}$ we prove a formula $DS(L) = \bigoplus \Pi^{n_i} L_i$ for the image of an arbitrary irreducible representation. In particular $DS(L)$ is semisimple and multiplicity free. We derive a few applications of this theorem such as the degeneration of certain spectral sequences and a formula for the modified superdimension of an irreducible representation.

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BibTeXRIS

Thorsten Heidersdorf, Rainer Weissauer. 2014-06-02. Cohomological Tensor Functors on Representations of the General Linear Supergroup. https://arxiv.org/abs/1406.0321

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