Dear J"urgen, I mailed a query to the GAP Forum a few days ago, but have not received any reply. Is it possible for you to look at this? Ravi Kulkarni
On Sat, Oct 31, 2009 at 6:56 PM, Ravi Kulkarni <ravi.k...@gmail.com> wrote: > Dear GAP Forum, > I need to calculate the image of a homomorphism of a matrix group: > > gap> m1 := [ [0,1,0],[-1,0,0],[0,0,1] ];; > gap> m2 := [ [0,1,0],[0,0,1],[1,0,0] ];; > gap> O := Group(m1,m2);; # one of the two 3-dim irrep of SymmetricGroup(4) > (S_4) > > # compute the five conjugacy classes and combine them into one list > # skip some code... > gap> ccall := Concatenation(cc1,cc2,cc3,cc4,cc5); > > I want to calculate the matrices corresponding to the two dimensional > irrep of S_4. Call this W. Examining the character table (and some > computation) shows that W is a representation of the quotient of S_4 > by the group generated by the elements of the fifth conjugacy class > (which has character 2 in the W representation). > > gap> H := Group(cc5);; > gap> IsNormal(O,H); > true > > gap> OmodH := FactorGroup(O,H); > Group([ f1, f2^2 ]) > > gap> hom := NaturalHomomorphismByNormalSubgroup(O,H); > CompositionMapping( [ (1,2,6,5), (1,2,3)(4,6,5) ] -> > [ f1, f2^2 ], <action isomorphism> ) > > Compute the images of elements of O: > > gap> imghom := List([1..Size(O)], i -> Image(hom,ccall[i])); > [ <identity> of ..., f1*f2, f1*f2, f1*f2^2, f1*f2^2, f1, f1, f2^2, f2, f2, > f2^2, f2, f2^2, f2, f2^2, f1, f1, f1*f2, f1*f2, f1*f2^2, f1*f2^2, > <identity> of ..., <identity> of ..., <identity> of ... ] > > Now, what I would like to have are the 2x2 matrices corresponding to > each of the elements of "imghom". I can guess what f1 and f2 are in > this example, but would be wary of doing so for a larger group. > > Is there a systematic way of getting the matrices f1 and f2? > > Thanks, > Ravi > _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
