proposition: Lemma cfDet_id xi : xi \is a linear_char -> cfDet xi = xi.
proof: Proof. move=> lin_xi; have /irrP[i Dxi] := lin_char_irr lin_xi. apply/cfun_inP=> x Gx; rewrite Dxi -irrRepr cfDetRepr !cfunE trace_mx11 mxE. move: lin_xi (_ x) => /andP[_]; rewrite Dxi irr1_degree pnatr_eq1 => /eqP-> X. by rewrite {1}[X]mx11_scalar det_scalar1 trace_mx11. 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)