Hi Vincent,
On Sat, Apr 11, 2020 at 08:05:35PM +0200, Vincent Delecroix wrote:
>
> I am looking for transitive groups G of S_d (I don't know d) with
> the following properties
>
> (*1) G admits an irreducible representation defined over
> QQ[sqrt(5)] (in particular the character is real)
>
> (*2) the stabilizer H of 1 in G admits invariant vectors
> in that irreducible representation.
>
> Question number one: knowing an irreducible representation defined
> over QQ[sqrt(5)] what is the fastest way to check for (*2)?
Do you also have d given at this moment? If not, one can argue
that for d=|G| one has that (*2) holds automatically:
indeed, take the regular permutation representation of G. Then the
QQ[sqrt(5)]-irreducible will be there, and H={1_G} will certainly
leave every vector there invariant.
HTH.
Best
Dima
>
> Best
> Vincent
>
> _______________________________________________
> Forum mailing list
> Forum@gap-system.org
> https://mail.gap-system.org/mailman/listinfo/forum
_______________________________________________
Forum mailing list
Forum@gap-system.org
https://mail.gap-system.org/mailman/listinfo/forum
