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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.

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