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Turning weight multiplicities into Brauer characters. (English) Zbl 1462.20007
The purpose of the paper is to describe two methods for computing \(p\)-modular Brauer character tables for groups of Lie type \(G(p^f)\) in defining characteristic \(p\), assuming that the ordinary character table of \(G(p^f)\) is known, and the weight multiplicities of the corresponding algebraic group \(\mathbf{G}\) are known for \(p\)-restricted highest weights. As an application of these methods some character tables are computed for the modular ATLAS project.

20C33 Representations of finite groups of Lie type
20C20 Modular representations and characters
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