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. Is there an efficient way that I can use these built-in GAP functions to determine if two matrices are in the same double-coset and/or enumerate a list of double-coset representatives? Thanks in advance for any help with this.
Katie Morrison _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
