proposition: Lemma cfRepr_standard n (rG : mx_representation algC G n) : cfRepr (standard_grepr rG) = \sum_i (standard_irr_coef rG (W i))%:R *: 'chi_i.
proof: Proof. rewrite cfRepr_dsum (reindex _ (socle_of_Iirr_bij _)). by apply: eq_bigr => i _; rewrite scaler_nat cfRepr_muln irrRepr. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype choice ssrnat seq) mathcomp(path div fintype tuple finfun bigop prime order) mathcomp(ssralg poly finset gproduct fingroup morphism) mathcomp(perm automorphism quotient finalg action zmodp) mathcomp(commutator cyclic center pgroup nilpotent sylow) mathcomp(abelian matrix mxalgebra mxpoly mxrepresentation) mathcomp(vector ssrnum algC classfun archimedean)