Let G be a simple Chevalley group defined over Fq. We show that if r does not divide q and k is an algebraically closed field of characteristic r, then very few irreducible kG-modules have nonzero H1(G, V). We also give an explicit upper bound for dim H1(G, V) for V an irreducible kG-module that does not depend on q, but only on the rank of the group. Cline, Parshall and Scott showed that such a bound exists when r|q. We obtain extremely strong bounds in the case that a Borel subgroup has no fixed points on V.
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty