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The Steinberg linkage class for a reductive algebraic group

Henning Haahr Andersen Aarhus, Denmark

Representation Theory mathscidoc:1912.43013

Arkiv for Matematik, 56, (2), 229 – 241, 2018
Let G be a reductive algebraic group over a field of positive characteristic and denote by C(G) the category of rational G-modules. In this note, we investigate the subcategory of C(G) consisting of those modules whose composition factors all have highest weights linked to the Steinberg weight. This subcategory is denoted ST and called the Steinberg component. We give an explicit equivalence between ST and C(G) and we derive some consequences. In particular, our result allows us to relate the Frobenius contracting functor to the projection functor from C(G) onto ST.
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@inproceedings{henning2018the,
  title={The Steinberg linkage class for a reductive algebraic group},
  author={Henning Haahr Andersen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204100942319565569},
  booktitle={Arkiv for Matematik},
  volume={56},
  number={2},
  pages={229 – 241},
  year={2018},
}
Henning Haahr Andersen. The Steinberg linkage class for a reductive algebraic group. 2018. Vol. 56. In Arkiv for Matematik. pp.229 – 241. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204100942319565569.
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