[GAP Forum] GAP4 question: character table as a matrix

Dmitrii Pasechnik dima at thi.informatik.uni-frankfurt.de
Wed Feb 4 03:47:46 GMT 2004

Dear Forum,

On Tue, Feb 03, 2004 at 07:57:38PM -0500, Roman Schmied wrote:
> 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?
> 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));
A vector of characters? You mean, a character?

for this purpose there are special functions available, 
you don't have to roll your own.
  ConstituentsOfCharacter( [<tbl>, ]<chi> ) 

  is  the set of irreducible characters that occur in the decomposition
  of the (virtual) character <chi> with nonzero coefficient.

ConstituentsOfCharacter( CharacterTable(g), c )

will do the job for you.


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