## Arkiv för Matematik

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

### The Steinberg linkage class for a reductive algebraic group

Henning Haahr Andersen

#### Abstract

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 $\mathcal{ST}$.

#### Article information

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

Dates
Revised: 27 December 2017
First available in Project Euclid: 19 June 2019

https://projecteuclid.org/euclid.afm/1560968131

Digital Object Identifier
doi:10.4310/ARKIV.2018.v56.n2.a2

Mathematical Reviews number (MathSciNet)
MR3893772

Zentralblatt MATH identifier
07021436

#### Citation

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. https://projecteuclid.org/euclid.afm/1560968131