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  Cohomological tensor functors on representations of the general linear supergroup

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

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Item Permalink: https://hdl.handle.net/21.11116/0000-0008-E157-8 Version Permalink: https://hdl.handle.net/21.11116/0000-000E-29A9-6
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https://doi.org/10.1090/memo/1320 (Publisher version)
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 Creators:
Heidersdorf, Thorsten1, Author           
Weissauer, Rainer, Author
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Representation Theory
 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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Language(s): eng - English
 Dates: 2021
 Publication Status: Issued
 Pages: v, 106
 Publishing info: Provindence, RI : American Mathematical Society
 Table of Contents: -
 Rev. Type: -
 Identifiers: arXiv: 1406.0321
DOI: 10.1090/memo/1320
ISBN: 978-1-4704-4714-4
 Degree: -

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Title: Memoirs of the American Mathematical Society
Source Genre: Series
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Pages: - Volume / Issue: 270, number 1320 Sequence Number: - Start / End Page: - Identifier: -