[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.
thanks
Dmitrii
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