Representation theory of finite groups of Lie type has made gigantic advances over the last twenty years. The powerful Deligne- Lusztig theory allows one to solve many questions about ordinary representations. The modular representation theory in the defining characteristic is closely related to the representation theory of Lie groups. It contains a lot of important results which make many particular problems accessible. However, extending explicit classical results to the modular case is usually a very difficult problem. In particular, computing the degrees of irreducible representations and weight multiplicities involves determining the maximal submodules of Weyl modules. Andersen's linkage principle [2] and Premet's theorem on weights [36] are among the most useful tools for studying particular representations.in general, the composition factors of Weyl modules can be read off from Lusztig's conjecture in combination with Jantzen's translation principle [28]. Lusztig's conjecture has been proved for large p: a major achievement of modular representation theory which combines profound results of Kazhdan and Lusztig, Casian, Kashiwara and Tanisaki, and Andersen, Jantzen and Soergel.
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