2012/01/25 by David I. Stewart, Stewart, David I.
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT
paper · pdf · doi:10.48550/arxiv.1201.5310
13 pages; v2 fixes some errors
arxiv created 2012/04/24 · arxiv updated 2012/04/25
Let G be an exceptional algebraic group defined over an algebraically closed field k of characteristic p>0 and let H be a subgroup of G. Then following Serre we say H is G-completely reducible or G-cr if, whenever H is contained in a parabolic subgroup P of G, then H is in a Levi subgroup of that parabolic. Building on work of Liebeck and Seitz, we find all triples (X,G,p) such that there exists a closed, connected, simple non-G-cr subgroup H<G with root system X.