End MoreVchar.
Definition dirr (gT : finGroupType) (B : {set gT}) : pred_class :=
[pred f : 'CF(B) | (f \in irr B) || (- f \in irr B)].
Arguments dirr {gT}.
Section Norm1vchar.
Variables (gT : finGroupType) (G : {group gT}).
Fact dirr_key : pred_key (dirr G). Proof. by []. Qed.
Canonical dirr_keyed := KeyedPred dirr_key.
Fact dirr_oppr_closed : oppr_closed (dirr G).

Lemma cfdot_dirr f g : f \in dirr G -> g \in dirr G ->
'[f, g] = (if f == - g then -1 else (f == g)%:R).