Properties of The (m, n) Irrep
Since the angular momentum operator is given by J = A + B, the highest weight of the rotation subrepresentation will be m + n. So for example, the (1/2,1/2) representation has spin 1. The (m, n) representation is (2m + 1)(2n + 1)-dimensional.
Read more about this topic: Representation Theory Of The Lorentz Group
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