Dear All, The first example I tried on GAP is about the symmetric group of 4 elements(?). I tried to get its irreducible matrix representation. The outcome I got from GAP is
gap> List(g,g->g^reps[3]); [ [ [ 1, 0 ], [ 0, 1 ] ], [ [ 0, E(3) ], [ E(3)^2, 0 ] ], [ [ E(3)^2, 0 ], [ 0, E(3) ] ], [ [ E(3), 0 ], [ 0, E(3)^2 ] ], [ [ 0, E(3)^2 ], [ E(3), 0 ] ], [ [ E(3), 0 ], [ 0, E(3)^2 ] ], [ [ 0, 1 ], [ 1, 0 ] ], [ [ 0, E(3) ], [ E(3)^2, 0 ] ], [ [ E(3)^2, 0 ], [ 0, E(3) ] ], [ [ 0, 1 ], [ 1, 0 ] ], [ [ E(3), 0 ], [ 0, E(3)^2 ] ], [ [ 1, 0 ], [ 0, 1 ] ], [ [ 0, 1 ], [ 1, 0 ] ], [ [ E(3)^2, 0 ], [ 0, E(3) ] ], [ [ 0, E(3) ], [ E(3)^2, 0 ] ], [ [ 0, E(3)^2 ], [ E(3), 0 ] ], [ [ E(3), 0 ], [ 0, E(3)^2 ] ], [ [ 0, E(3)^2 ], [ E(3), 0 ] ], [ [ 1, 0 ], [ 0, 1 ] ], [ [ E(3)^2, 0 ], [ 0, E(3) ] ], [ [ 0, E(3) ], [ E(3)^2, 0 ] ], [ [ 1, 0 ], [ 0, 1 ] ], [ [ 0, E(3)^2 ], [ E(3), 0 ] ], [ [ 0, 1 ], [ 1, 0 ] ] ] My question is: (1) How do I know which matrix corresponds to which group element? (2) What does E(3) mean? (3) There can be different representations which has all matrix elements real, how can I find a similarity transformation which can do this? (4) Can the output be set in a way that these 24 matrices can be read in directly by say Fortran? Thank you very much, Sincerely, Jon _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
