Dear Krishna, The answer to your question is yes. You may get different representations for different trials even for solvable groups. For solvable groups, the only case that you will get the same answer is when it doesn't need to extend a representation.
I hope it helps. Regards Vahid ____________________________________________ Program Director Modelling of Complex Social Systems (MoCSSy) The IRMACS Centre (ASB 10905) Simon Fraser University, BC Canada Tel: 778-782-7854 http://mocssy.irmacs.sfu.ca/ ----- Original Message ----- From: "krishna mohan" <trebauchet1...@yahoo.co.in> To: "gap forum" <fo...@gap-system.org> Sent: Sunday, October 10, 2010 5:29:01 AM Subject: [GAP Forum] Using repsn package on A5 Hi.... I do the following: gap> g:=AllSmallGroups(60)[5]; Group([ (1,2,3,4,5), (1,2,3) ]) gap> StructureDescription(g); "A5" gap> LoadPackage("repsn"); true gap> chi:=Irr(g);; gap> rep1:=IrreducibleAffordingRepresentation(chi[4]); [ (1,2)(3,4), (1,4)(2,3), (1,3)(4,5) ] -> [ [ [ E(3), -1/2*E(3)^2, -1/2*E(3)+1/2*E(3)^2, 1/2*E(3)^2 ], [ 1, -E(3), E(3)^2, -E(3)^2 ], [ E(3), 1/2*E(3), 1/2*E(3)^2, -1/2*E(3) ], [ E(3), -E(3)-1/2*E(3)^2, -3/2*E(3)-1/2*E(3)^2, -1/2*E(3)^2 ] ], [ [ E(3)^2, 1/2*E(3), E(3)-1/2*E(3)^2, -1/2*E(3) ], [ 0, -1/2*E(3), -E(3)-1/2*E(3)^2, -1/2*E(3)-E(3)^2 ], [ E(3)^2, -1/2*E(3)^2, 1/2*E(3)-1/2*E(3)^2, 1/2*E(3)^2 ], [ 1, -E(3)-1/2*E(3)^2, -1/2, -1/2*E(3)^2 ] ], [ [ 1, -1/2*E(3)+1/2*E(3)^2, 1/2*E(3)+E(3)^2, 1/2*E(3)-1/2*E(3)^2 ], [ 0, -1, -1, -E(3) ], [ 0, 0, 0, E(3) ], [ 0, 0, E(3)^2, 0 ] ] ] gap> rep2:=IrreducibleAffordingRepresentation(chi[4]); [ (1,2)(3,4), (1,4)(2,3), (1,3)(4,5) ] -> [ [ [ 1/2*E(3), -1/2*E(3)-E(3)^2, E(3)^2, 1/2*E(3)^2 ], [ 0, -E(3)^2, E(3)^2, E(3) ], [ E(3)+1/2*E(3)^2, -3/2*E(3)^2, E(3)^2, 1/2*E(3)-1/2*E(3)^2 ], [ 1/2*E(3)-1/2*E(3)^2, -1/2*E(3)+1/2*E(3)^2, 0, -1/2*E(3) ] ], [ [ -1/2, 1/2, E(3), -1/2*E(3)-E(3)^2 ], [ 1/2*E(3)+E(3)^2, 1/2*E(3), 1, -1/2*E(3)^2 ], [ 1/2*E(3)+E(3)^2, -1/2*E(3)-E(3)^2, 0, -1/2*E(3)^2 ], [ -1/2*E(3)-E(3)^2, -3/2*E(3), E(3), -E(3)-1/2*E(3)^2 ] ], [ [ -1/2*E(3), 1/2*E(3)+E(3)^2, 0, E(3)+1/2*E(3)^2 ], [ 1/2*E(3), -1/2*E(3), E(3), -1/2*E(3)^2 ], [ -1/2*E(3)^2, -E(3)+1/2*E(3)^2, E(3), 1/2 ], [ E(3)^2, -1, 1, 0 ] ] ] As one can see, the representation matrices are different in the two instances. I tried this with a couple of other groups, but always got the same representation matrices. On going through the repsn manual, it seemed to me that this must be due to the fact that A5 is not solvable. So, if the group is solvable, then does the program always give the same representation matrices? Or is it that the matrices generated may be different for different trials even for a solvable group? Krishnamohan P _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
