Dear all, I'm looking for the 2-dimensional unitary representation of SL(2,5). I thought GAP would give it to me, but gap> rep := First(IrreducibleRepresentations(SL(2,5)),r->Length(Image(r).1)=2); CompositionMapping( [ (2,5,4,3)(6,11,16,21)(7,15,19,23)(8,12,20,24)(9,13,17,25)(10,14,18,22), (2,16,9)(3,21,15)(4,6,17)(5,11,23)(7,22,10)(8,12,13)(14,18,19)(20,24,25) ] -> [ [ [ -E(5)+E(5)^4, E(5)^2+E(5)^3 ], [ E(5)^2+E(5)^3, E(5)-E(5)^4 ] ], [ [ E(5)+E(5)^2, -E(5)^2-E(5)^3 ], [ 1, E(5)^3+E(5)^4 ] ] ], <action isomorphism> )
does *not* give unitary matrices. Now, classically, I can define s = Sum(SL(2,5),g->g^rep*TransposedMat(ComplexConjugate(g^rep))), which is the Gram matrix of a positive-definite invariant sesquilinear form; but I don't know how to factor s as t*TransposedMat(ComplexConjugate(t)) so as to conjugate rep by t. Any ideas? Thanks in advance, Laurent _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
