proposition: Lemma max_cfRepr_norm_scalar n (rG : mx_representation algC G n) x : x \in G -> `|cfRepr rG x| = cfRepr rG 1%g -> exists2 c, `|c| = 1 & rG x = c%:M.
proof: Proof. move=> Gx; have [e [[B uB def_x] [_ e1] [-> _] _]] := repr_rsim_diag rG Gx. rewrite cfRepr1 -[n in n%:R]card_ord -sumr_const -(eq_bigr _ (in1W e1)). case/normC_sum_eq1=> [i _ | c /eqP norm_c_1 def_e]; first by rewrite e1. have{} def_e: e = const_mx c by apply/rowP=> i; rewrite mxE def_e ?andbT. by exists c => //; rewrite def_x def_e diag_const_mx scalar_mxC mulmxKV. 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)