[GAP Forum] Specht modules for S_n

[Juergen Mueller]

Dear Forum,

This is just to let you know that I have answered Dima's question
encluded below already a few days ago; subsequently we had a brief
private eMail correspondence. Accidentally, my original reply has
not been sent to the Forum as well; apologies for that.

Merry Christmas, and all the best for the New Year,

J"urgen

>   Date: Fri, 25 Nov 2005 18:12:44 +0100
>   From: Dima Pasechnik <d.v.pasechnik at uvt.nl>
>   Subject: [GAP Forum] Specht modules for S_n
>   To: Forum at gap-system.org
>
> Dear Forum,
> I need some efficient basic functionality for irreducible
> representations
> of S_n. I understand it is available in GAP3 (SPECHT package), but not
> in
> GAP4.
> Is it feasible to contruct and
> to work with Q-modules of dimension few hundred using
> this package?
>
> A naive implementation of constrution of Specht modules runs into
> a problem that one needs to operate on
> the set of tableaux, that get pretty large.
> (The Specht module will be a proper submodule of the (huge)
>  permutation module on the tableaux, spanned by the Young symmetrizers
>  of the standard tableaux)
>
> I suspect that using a "straightening algorithm", that allows
> to work with standard tableaux only, should be more efficient.
>
> (Or perhaps I am missing some  obvious efficient method to build these
>  representations?)
>
> Did anyone have any experience with such implementations?
>
> thanks,
> Dima