[GAP Forum] Group representations over finite fields

[Juergen Mueller]

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
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