Dear Forum,
It's double coset week! On Jan 12, 2011, at 1/12/11 1:07, Katie Morrison wrote: > I am trying to compute double cosets within the orthogonal group with > similitudes (which I am taking to be the set of matrices that satisfy > MM^T=\lambda *I where I is the identity and \lambda is a non-zero scalar). > I have obtained the orthogonal group with similitudes by starting with > GO(n,q), conjugating it by an appropriate change of basis matrix to get the > matrices that preserve the standard dot product rather than the bilinear > form that GAP uses, and then taking the normalizer of this group in > GL(n,q). > Using this construction of the orthogonal group with similitudes, > I would like to then find double cosets of certain subgroups of this, but as > far as I know GAP only has the double-cosets function implemented for > permutation groups. Since the normalizer calculation succeeded, it seems your parameters are small enough to allow for the construction of a permutation representation. In this situation you will be able to use this representation and permutation group functionality to get the results. For example, if G is the normalizer and A and B are the two subgroups, the following commands would get you double coset information in the matrix group: hom:=IsomorphismPermGroup(G); Gperm:=Image(hom,G); Aperm:=Image(hom,A); Bperm:=Image(hom,B); dc:=DoubleCosetRepsAndSizes(Gperm,Aperm,Bperm); List(dc,x->[PreImagesRepresentative(hom,x[1]),x[2]]); Best wishes, Alexander Hulpke -- Colorado State University, Department of Mathematics, Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA email: hul...@math.colostate.edu, Phone: ++1-970-4914288 http://www.math.colostate.edu/~hulpke _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
