proposition: Lemma lin_char_reprP xi : reflect (exists rG : mx_representation algC G 1, xi = cfRepr rG) (xi \is a linear_char).
proof: Proof. apply (iffP idP) => [xiL | [rG ->{xi}]]. - have:= lin_charW xiL => /char_reprP[[drG rG /= Hxi]]. have /eqP:= lin_char1 xiL; rewrite Hxi cfRepr1 pnatr_eq1=> /eqP drG1. by subst drG; exists rG. - exact: cfRepr1_lin_char. Qed.
imports: mathcomp(all_ssreflect) mathcomp(fingroup perm ssralg morphism perm action) mathcomp(zmodp) mathcomp(vector matrix mxalgebra ssrnum algC) mathcomp(mxrepresentation classfun character) permcomp tools partition congr cycles cycletype presentSn