On the ℓ-modular composition factors of the Steinberg representation [article]

Meinolf Geck
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
more » ... _k when G=_n(q) or G is a finite classical group and ℓ is a so-called linear prime.
arXiv:1504.04157v2 fatcat:jrovls6t5vep7ih2m2cvr5rszy