TY - JOUR
T1 - Reducible subgroups of exceptional algebraic groups
AU - Litterick, Alastair J.
AU - Thomas, Adam R.
PY - 2019/6/1
Y1 - 2019/6/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85053716011&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2018.09.004
DO - 10.1016/j.jpaa.2018.09.004
M3 - Article (Academic Journal)
AN - SCOPUS:85053716011
SN - 0022-4049
VL - 223
SP - 2489
EP - 2529
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 6
ER -