Section AutChar.
Variables (gT : finGroupType) (G : {group gT}).
Implicit Type u : {rmorphism algC -> algC}.
Implicit Type chi : 'CF(G).
Let xiMV x : x \in G -> xi x * xi (x^-1)%g = 1.
End OneChar.
Fact linear_char_key B : pred_key (@linear_char B). Proof. by []. Qed.
Canonical linear_char_keted B := KeyedQualifier (linear_char_key B).
Fact linear_char_divr : divr_closed (@linear_char G).
Canonical lin_char_mulrPred := MulrPred linear_char_divr.
Canonical lin_char_divrPred := DivrPred linear_char_divr.
Variables (A : {group aT}) (G : {group gT}).

(* This is Isaacs, Lemma (2.15) (d). *)
Lemma char_inv (chi : 'CF(G)) x : chi \is a character -> chi x^-1%g = (chi x)^*.