Definition gring_irr_mode_def (i : Iirr G) := ('chi_i 1%g)^-1 *: 'chi_i.
Definition gring_irr_mode := locked_with gring_irr_mode_key gring_irr_mode_def.
Canonical gring_irr_mode_unlockable := [unlockable fun gring_irr_mode].
End GenericClassSums.
Arguments gring_irr_mode {gT G%G} i%R _%g : extra scopes.
Notation "''K_' i" := (gring_class_sum _ i)
(at level 8, i at level 2, format "''K_' i") : ring_scope.
Notation "''omega_' i [ A ]" := (xcfun (gring_irr_mode i) A)
(at level 8, i at level 2, format "''omega_' i [ A ]") : ring_scope.
Section IntegralChar.
Variables (gT : finGroupType) (G : {group gT}).

(* This is Isaacs, Corollary (3.6). *)
Lemma Aint_char (chi : 'CF(G)) x : chi \is a character -> chi x \in Aint.