“…Let us remark that acts trivially on . Therefore, according to this lemma, when the characteristic of is either zero or prime with the order of , that is when it is prime with any of the weights , induces the isomorphism More generally, for every , induces the isomorphism In order to get the properties stated in [All22a, Appendix A] back, let us show the commutativity of the following diagram:
where and and the actions of the group on and are coordinate-wise. Let us show that the top in (4) is well-defined, that is, is -equivariant.…”