[GAP Forum] Group representations over finite fields

[Alexander Hulpke]

Dear Forum, Dear Franciois Le Gall,

This is a known bug that will be fixed in the next release. It is limited to CollectedFactors (none of the other meataxe functions, and thus no other GAP functionality is affected) and most times only will have produced overcounts, but in rare cases might have missed irreducible factors.

What happened is that if a small submodule is found (dimension <1/10 total, GAP tries to factor out not only this module, but all isomorphic submodules, using `Homomorphisms'. However the length of the list returned by homomorphisms is not the number of isomorphic composition factors, in particualr if there are module automorphisms.

Apologies for the problem!

Alexander Hulpke

On Aug 5, 2011, at 10:19 AM, Francois Le Gall 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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