Dear Francois, in principle, this is the right way. Alone, the MeatAxe routines you are invoking are randomized, so that you get *essentially* the same answer each time, that is up to order of the constituents and up to equivalence.
Still, as you are interested in representation degrees and multiplicities in the non-modular situation, you can reduce to computing the ordinary character table of G, and just have to deal with Galois descent to the (possibly non-splitting) prime field. This should, for medium-sized and maybe even for smallish groups be much faster than computing the irreducible representations explicitly. Hope that helps. If you need more specific help please do not hesitate to ask again. Best wishes, J"urgen M"uller On Thu, Aug 04, 2011 at 02:32:07PM +0900, Francois Le Gall wrote: > Dear Forum, > > I am currently investigating the dimensions of the irreducible > representations of a (small) finite group G over the finite field GF(p) when > p does not divide the order of G, along with their multiplicities in the > regular representation of G. This is the first time I use GAP for > representation theory over finite fields, and I would be very happy to know > if there is a simple way to obtain this information. > > I read the MeatAxe documentation and tried the following commands > > R:=RegularModule(G,GF(p)); > MTX.CollectedFactors(R[2]); > > but I suspect that this is different from what I am looking for > (specifically, for G:=AbelianGroup([8,4]) and p:=3, each call to > MTX.CollectedFactors(R[2]) seems to give a different answer). > > Thank you in advance. > > Sincerely, > > Francois Le Gall > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
