[GAP Forum] Group representations over finite fields

[Asst. Prof. Dmitrii (Dima) Pasechnik]

By the way, I tried this on a 64-bit (Intel) Linux, and also had
diverging results over several tries.

On 5 August 2011 16:19, Francois Le Gall <legall at is.s.u-tokyo.ac.jp> wrote:
> Dear Juergen, Dear Forum,
>
> Thank you very much for the very helpful explanations!
> I will try to work out the details of the reduction from the ordinary character tables you suggested.
>
> I now understand that MeatAxe procedures are randomized. There is nevertheless something that I feel very strange.
> When I run (using GAP 4.4.12 on Mac OS X 10.6.8)  several times the following commands
>
> G:=AbelianGroup([8,4]);
> R:=RegularModule(G,GF(3));
> F:=MTX.CollectedFactors(R[2]);
>
> I obtain five kinds of outputs:
>
> (a) 4 irreducibles of dimension 1 (each with multiplicity 1) + 14 irreducibles of dimension 2 (each with multiplicity 1)
> (b) 4 irreducibles of dimension 1 (each with multiplicity 1) + 13 irreducibles of dimension 2 (each with multiplicity 1) + 1 irreducibles of dimension 2 (with multiplicity 2)
> (c) 4 irreducibles of dimension 1 (each with multiplicity 1) + 12 irreducibles of dimension 2 (each with multiplicity 1) + 2 irreducibles of dimension 2 (each with multiplicity 2)
> (d) 4 irreducibles of dimension 1 (each with multiplicity 1) + 11 irreducibles of dimension 2 (each with multiplicity 1) + 3 irreducibles of dimension 2 (each with multiplicity 2)
> (e) 4 irreducibles of dimension 1 (each with multiplicity 1) + 9 irreducibles of dimension 2 (each with multiplicity 1) + 5 irreducibles of dimension 2 (each with multiplicity 2)
>
> Outputs (b) to (e) seem wrong (specifically, the sum of the products of dimensions by multiplicities does not match the order of the group). Does this mean that the command
> MTX.CollectedFactors outputs, with some probability, wrong multiplicities?
>
> Best regards,
>
> Francois Le Gall
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Dmitrii Pasechnik
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