Cohomological tensor functors on representations of the general linear 
supergroup

Heidersdorf, Thorsten; Weissauer, Rainer

doi:10.1090/memo/1320

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Cohomological tensor functors on representations of the general linear supergroup

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Heidersdorf, Thorsten
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1090/memo/1320
(Publisher version)

https://doi.org/10.48550/arXiv.1406.0321
(Preprint)

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Citation

Heidersdorf, T., & Weissauer, R. (2021). Cohomological tensor functors on representations of the general linear supergroup. Provindence, RI: American Mathematical Society.

Cite as: https://hdl.handle.net/21.11116/0000-0008-E157-8

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.