proposition: Lemma cfcenter_eq_center (i : Iirr G) : ('Z('chi_i)%CF / cfker 'chi_i)%g = 'Z(G / cfker 'chi_i)%g.
proof: Proof. apply/eqP; rewrite eqEsubset; rewrite cfcenter_subset_center ?irr_char //. apply/subsetP=> _ /setIP[/morphimP[x /= _ Gx ->] cGx]; rewrite mem_quotient //=. rewrite -irrRepr cfker_repr cfcenter_repr inE Gx in cGx *. apply: mx_abs_irr_cent_scalar 'Chi_i _ _ _; first exact/groupC/socle_irr. have nKG: G \subset 'N(rker 'Chi_i) by apply: rker_norm. apply/centgmxP=> y Gy; rewrite [eq]lock -2?(quo_repr_coset (subxx _) nKG) //. move: (quo_repr _ _) => rG; rewrite -2?repr_mxM ?mem_quotient // -lock. by rewrite (centP cGx) // mem_quotient. 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)