Dear Gabor, Willem, Peter, all, Indeed I took the Peter's question as if he didn't mind the field to be extended.
But even if he did, there are tools available for dealing with Q-irreducible representations, e.g. the Artin's theorem that basically says that the character of a rational representation is a difference of permutation characters, each of the latter a direct sum of representations induced from a cyclic subgroup, and the related counting result that says that the number of irreducible Q-representations equals the number of conjugate cyclic subgroups. So it does not look completely hopeless to construct all the Q-irreducibles, if needed. Regards, Dima 2008/9/27 Gabor Ivanyos <[EMAIL PROTECTED]>: > Dear Dima, Willem, Peter, all, >> Formulae for this can be found in Serre's book "Linear representations >> of finite groups." Springer GTM, Vol. 42. > I think Peter was asking for decomposition over Q. Let us stress "over Q"`. > I agree Willem in that it is hard in general. For finite groups it mght be ber > somewhat easier than the general case, but I am not aware of any serious > result supportimg this. > Gabor > _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
