Section Char.
Variables (gT : finGroupType) (G : {group gT}).
Fact cfRepr_subproof n (rG : mx_representation algCF G n) :
is_class_fun <<G>> [ffun x => \tr (rG x) *+ (x \in G)].
Definition cfRepr n rG := Cfun 0 (@cfRepr_subproof n rG).
End StandardRepr.
Definition cfReg (B : {set gT}) : 'CF(B) := #|B|%:R *: '1_[1].
Definition xcfun (chi : 'CF(G)) A :=
(gring_row A *m (\col_(i < #|G|) chi (enum_val i))) 0 0.
Canonical xcfun_r_additive A := Additive (xcfun_r_is_additive A).

Lemma xcfunZl a phi A : xcfun (a *: phi) A = a * xcfun phi A.