Hi All, Thank you very much for your answers and hints ! I have to study it and try in GAP.
Frankly speaking I am having doubts whether I understand when set of vectors form root system and how to decompose Lie algebra into root subspaces. In the real compact case these subspaces are 2-dimensional. For example for compact e6 there is decomposition into 6-dimensional Cartan algebra and 36 2-dimensional subspaces Vi. My hypothesis is that [Vi,Vj]=Vk for some k. Corresponding roots satisfy condition ri+rj=rk or ri-rj=rk. If you take two perpendicular vectors v,w from Vi, then [v,w] = ri and <v,w,ri> is isomorfic to su2. Is this hypothesis true ? Regards, Marek Mitros U¿ytkownik Frank Lübeck <[EMAIL PROTECTED]> napisa³: >On Mon, Nov 05, 2007 at 12:41:59PM +0100, [EMAIL PROTECTED] wrote: >> Dear Marek Mitros, >> >> >1. Do you have any ideas for building matrix representations of >> >compact e7, e8 in dimensions 56,248 respectively ? >> >> Unfortunately I do not, but maybe somebody else does. > >Dear Forum, > >Just for the records: I have sent Marek generating matrices, including some >which generate the subgroups he was looking for. > >Best regards, > > Frank > >-- >/// Dr. Frank Lübeck, Lehrstuhl D für Mathematik, Templergraben 64, /// >\\\\\\ 52062 Aachen, Germany \\\\\\ >/// E-mail: [EMAIL PROTECTED] /// >\\\\\\ WWW: http://www.math.rwth-aachen.de/~Frank.Luebeck/ \\\\\\ > >_______________________________________________ >Forum mailing list >[email protected] >http://mail.gap-system.org/mailman/listinfo/forum > _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
