[GAP Forum] Decomposing rational modules

[Asst. Prof. Dmitrii (Dima) Pasechnik]

Dear Peter, dear all,
Is not so hard to implement the classical formulae for homogeneous
components (i.e. the components that are direct sums of isomorphic copies of
a particular irreducible), etc. The projectors are appropriate linear
combinations
of conjugacy class sums.

In fact I am working at the moment on a GAP package that constructs the
coherent configuration of a not necessarily transitive permutation group
and computes its irreducible representations --- as a by-product one would get
a decomposition of the permutation module into irreducibles...
I have (re)invented an efficient way to compute the conjugacy class
sums, along the way.

HTH,
Dima

2008/9/26 Peter Cameron <p.j.cameron at qmul.ac.uk>:
> Dear Forum,
>
> Is there a simple way to decompose rational permutation modules? A quick
> browse of the manual suggests that one can decompose modules over finite
> fields (I suppose this uses the MeatAxe) but not over the rationals
> (which I naively thought would be easier).
>
> In particular cases one can spot a vector in each submodule and then take
> the sumbodule spanned by its images, but it would be nice to have something
> more general...
>
> Peter Cameron.
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>