did I tell you that I suspect that Alt2(Alt2(V)) is the Schur (3,1) functor, and then since V * Alt3(V) = Schur(3,1)(V) + Alt4(V), if V has dimension 3 then you get V * det(V) = Alt2(Alt2(V)) which could show that you almost get momentum back if you do Alt2 of the angular momentum