1. The problem statement, all variables and given/known data Find the generators of the four dimensional irreducible representation of SO(3), such that J_3 is diagonal. 3. The attempt at a solution I know how to get the rest if I know J_3, by using ladder operators. But what is J_3? For a 3d representation it's diagonal with 1,0-1, in 4d would it be 3/2, 1/2, -1/2 -3/2? Wasn't orbital angular momentum supposed to be of integer values, or did I forget QM so bad? Thanks for any help ------- nevermind, it is obviously not necessarily orbital angular momentum so that works..