2018/01/28 by Litterick, Alastair J., Thomas, Adam R.
#20G07 #20G10 (Secondary) #20G41 (Primary) #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1801.09266
Let G be a simple algebraic group over an algebraically closed field. A closed subgroup H of G is called G-completely reducible (G-cr) if, whenever H is contained in a parabolic subgroup P of G, it is contained in a Levi factor of P. In this paper we complete the classification of connected G-cr subgroups when G has exceptional type, by determining the L0-irreducible connected reductive subgroups for each simple classical factor L0 of a Levi subgroup of G. As an illustration, we determine all reducible, G-cr semisimple subgroups when G has type F4 and various properties thereof. This work complements results of Lawther, Liebeck, Seitz and Testerman, and is vital in classifying non-G-cr reductive subgroups, a project being undertaken by the authors elsewhere.