Dear Laurent, Dear Forum,
In principle (in recent versions of GAP, this got added later), adding the option `unitary’, i.e. IrreducibleRepresentations(SL(2,5):unitary); will produce unitary representations. > 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. This is a Cholesky decomposition, which (Wikipedia be thanked) seems to be a standard operation in the numerical world, and this is exactly what GAP uses. However in your concrete example this fails yet — the reason is that the Cholesky decomposition requires square roots, and the existing code for CholeskyDecomp in GAP cannot deal with square roots for irrationals. (It would have to construct a larger field etc. which makes the code far more complicated.) Anyhow, this might tell you how to do it by hand. Best, Alexander > > Any ideas? > > Thanks in advance, Laurent > _______________________________________________ > 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
