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James' Submodule Theorem and the Steinberg Module
Symmetry, integrability and geometry: methods and applications, Tome 13 (2017) Cet article a éte moissonné depuis la source Math-Net.Ru

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James' submodule theorem is a fundamental result in the representation theory of the symmetric groups and the finite general linear groups. In this note we consider a version of that theorem for a general finite group with a split $BN$-pair. This gives rise to a distinguished composition factor of the Steinberg module, first described by Hiss via a somewhat different method. It is a major open problem to determine the dimension of this composition factor.
Keywords: groups with a $BN$-pair; Steinberg representation; modular representations. 
@article{SIGMA_2017_13_a90,
     author = {Meinolf Geck},
     title = {James' {Submodule} {Theorem} and the {Steinberg} {Module}},
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     year = {2017},
     volume = {13},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a90/}
}
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Meinolf Geck. James' Submodule Theorem and the Steinberg Module. Symmetry, integrability and geometry: methods and applications, Tome 13 (2017). http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a90/

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