Section Stabiliser.
Variables (m : nat) (U : 'M[R]_(m, n)).
Canonical rconj_repr := MxRepresentation rconj_mx_repr.
Local Notation rGB := rconj_repr.
Canonical quo_repr := MxRepresentation quo_mx_repr.
Local Notation rGH := quo_repr.
Canonical regular_repr := MxRepresentation regular_mx_repr.
Local Notation aG := regular_repr.
Definition group_ring := enveloping_algebra_mx aG.
Local Notation R_G := group_ring.
Definition gring_row : 'M[R]_nG -> 'rV_nG := row (gring_index 1).
Canonical gring_row_linear := [linear of gring_row].

Lemma gring_row_mul A B : gring_row (A *m B) = gring_row A *m B.