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
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