Rights statement: The final, definitive version of this article has been published in the Journal, Journal of Algebra 389, 2013, © ELSEVIER.
Accepted author manuscript, 367 KB, PDF document
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - KW-sections for Vinberg's θ-groups of exceptional type
AU - Levy, Paul
N1 - The final, definitive version of this article has been published in the Journal, Journal of Algebra 389, 2013, © ELSEVIER.
PY - 2013/9/1
Y1 - 2013/9/1
N2 - Let k be an algebraically closed field of characteristic not equal to 2 or 3, let G be an almost simple algebraic group of type F4, G2 or D4 and let \theta be an automorphism of G of finite order, coprime to the characteristic. In this paper we consider the \theta-group (in the sense of Vinberg) associated to these choices; we classify the positive rank automorphisms via Kac diagrams and we describe the little Weyl group in each case. As a result we show that all -groups in types G2, F4 and D4 have KW-sections, confirming a conjecture of Popov in these cases.
AB - Let k be an algebraically closed field of characteristic not equal to 2 or 3, let G be an almost simple algebraic group of type F4, G2 or D4 and let \theta be an automorphism of G of finite order, coprime to the characteristic. In this paper we consider the \theta-group (in the sense of Vinberg) associated to these choices; we classify the positive rank automorphisms via Kac diagrams and we describe the little Weyl group in each case. As a result we show that all -groups in types G2, F4 and D4 have KW-sections, confirming a conjecture of Popov in these cases.
KW - Algebraic groups
KW - Lie algebras
KW - Automorphisms
KW - Invariant theory
KW - Pseudo-reflection groups
U2 - 10.1016/j.jalgebra.2013.04.035
DO - 10.1016/j.jalgebra.2013.04.035
M3 - Journal article
VL - 389
SP - 78
EP - 97
JO - Journal of Algebra
JF - Journal of Algebra
SN - 0021-8693
ER -