[GAP Forum] decomposition formulae for C-representations

Dmitrii Pasechnik dima at thi.informatik.uni-frankfurt.de
Tue Apr 6 09:56:03 BST 2004

Dear Forum,

are the formulae that give the decomposition of a C-represenation p
of a finite group G into direct sums of irreducibles implemented in GAP?
(perhaps somewhere within character theory machinery I guess)

I mean the standard ones given in e.g. Serre's "Linear Representations
of Finite Groups", Sect. 2.6 and 2.7.
For instance to obtain the subrepresentation of p (a direct sum of 
irreducible representations with the same character chi) of dimension 
n_chi, corresponding to the irrducible character chi, one uses the projection 
	n_chi/|G| sum_{g in G} chi^*(g)p(g) 
(Thm. 8 in Sect. 2.6 of the Serre's book)

Certainly, this is only feasible for groups of relatively small order
to use these formulae directly, but in our case the groups
are of order <10^4.


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