Arkiv för Matematik

  • Ark. Mat.
  • Volume 56, Number 2 (2018), 229-241.

The Steinberg linkage class for a reductive algebraic group

Henning Haahr Andersen

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Let $G$ be a reductive algebraic group over a field of positive characteristic and denote by $\mathcal{C}(G)$ the category of rational G-modules. In this note, we investigate the subcategory of $\mathcal{C}(G)$ consisting of those modules whose composition factors all have highest weights linked to the Steinberg weight. This subcategory is denoted $\mathcal{ST}$ and called the Steinberg component. We give an explicit equivalence between $\mathcal{ST}$ and $\mathcal{C}(G)$ and we derive some consequences. In particular, our result allows us to relate the Frobenius contracting functor to the projection functor from $\mathcal{C}(G)$ onto $\mathcal{ST}$.

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Ark. Mat., Volume 56, Number 2 (2018), 229-241.

Received: 1 September 2017
Revised: 27 December 2017
First available in Project Euclid: 19 June 2019

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Andersen, Henning Haahr. The Steinberg linkage class for a reductive algebraic group. Ark. Mat. 56 (2018), no. 2, 229--241. doi:10.4310/ARKIV.2018.v56.n2.a2.

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