[GAP Forum] Decomposing rational modules
Asst. Prof. Dmitrii (Dima) Pasechnik
dima at ntu.edu.sg
Fri Sep 26 11:26:02 BST 2008
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
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.
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.
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