Section DetRepr.
Variables (n : nat) (rG : mx_representation [fieldType of algC] G n).
Definition det_repr_mx x : 'M_1 := (\det (rG x))%:M.
Fact det_is_repr : mx_repr G det_repr_mx.
Canonical det_repr := MxRepresentation det_is_repr.
Definition detRepr := cfRepr det_repr.

Lemma detRepr_lin_char : detRepr \is a linear_char.