[GAP Forum] GAP4 question: character table as a matrix
Alexander Hulpke
hulpke at math.colostate.edu
Wed Feb 4 02:32:04 GMT 2004
Dear Roman Schmied,
> I am trying to use a character table of a permutation group "g" as a
> matrix, for further matrix multiplications. In order to extract this
> matrix, my code is
>
> TransposedMat(TransposedMat(Irr(CharacterTable(g))));
>
> which is very roundabout. Would anyone know of a nice way of doing this?
The following is probably the shortest
List(Irr(g),ShallowCopy);
though
n:=Length(Irr(g));Irr(g){[1..n]}{[1..n]};
is a close contender.
> My goal is the decomposition of a vector "c" of characters into a direct
> sum of irreducible representations, which I then do with
>
> TransposedMat(TransposedMat(Irr(CharacterTable(g))))
> * DiagonalMat(SizesConjugacyClasses(CharacterTable(g)))
> * c
> / Length(Elements(g));
As you have irreducible characters calculating scalar products will be
easier and more efficient:
MatScalarProducts(Irr(g),[c]);
or List(Irr(g),i->ScalarProduct(i,c));
(If you prefer to solve a system of equations,
SolutionMat(Irr(g),c);
will work.)
Best wishes,
Alexander Hulpke
-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke
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