On Certain Fixed Point Subgroups of Affine Kac-Moody Groups

AbstractIn this paper we give a detailed description of the fixed point subgroups of certain Kac-Moody groups under particular automorphisms. We consider Kac-Moody groups arising from simply laced extended Cartan matrices and their fixed point subgroups under automorphisms which contain a non-trivial field automorphism constituent as well as a non-trivial graph automorphism constituent. We show that such a situation satisfies all the conditions of a theorem of J-Y. Hée ["Torsion de groupes munis d′une donnée radicelle, Théorème (4.5)"] which concludes that the fixed point subgroup has a (B, N)-pair and a system of root subgroups. This paper contains some of the results in the author′s doctoral thesis ["On Some Twisted Kac-Moody Groups"]