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On the ℓ-modular composition factors of the Steinberg representation
[article]
2015
arXiv
pre-print
Let G be a finite group of Lie type and _k be the Steinberg representation of G, defined over a field k. We are interested in the case where k has prime characteristic ℓ and _k is reducible. Tinberg has shown that the socle of _k is always simple. We give a new proof of this result in terms of the Hecke algebra of G with respect to a Borel subgroup and show how to identify the simple socle of _k among the principal series representations of G. Furthermore, we determine the composition length of
arXiv:1504.04157v2
fatcat:jrovls6t5vep7ih2m2cvr5rszy