A Realization of Certain Affine Kac-Moody Groups of Types II and III Original Research Article

The aim of this paper is, in the notation of Kac, to extend results about Kac-Moody algebras to corresponding groups by proving that certain affine Kac-Moody groups of types II and III arise as the fixed point subgroups of affine Kac-Moody groups of type I of higher rank under particular automorphisms. We prove an analogue of a theorem of Hée which enables us to deduce some results about the fixed point subgroups of Kac-Moody groups arising from simply-laced extended Cartan matrices under automorphisms which are the product of a graph and a diagonal automorphism. We then prove that the groups obtained in this way are in fact isomorphic to Kac-Moody groups arising from affine Cartan matrices which are not of extended type. This paper contains the main results in the author′s doctoral thesis.