Irreducible representations of Poincaré group

Solution 1:

You could try to look at:

• Geometry of Quantum Theory - V. S. Varadarajan - Second Edition, on Chapter 9 (Relativistic Free Particles), in particular to the Theorem 9.4 (p.347), that is the classification theorem obtained by Wigner.
• A course in abstract harmonic analysis - G. B. Folland, on Chapter 6 (Induced Representations), in particular in the section 6.7.3 (The Poincaré Group, p.190).

Solution 2:

Here is an article that explains Wigner's classification (but not in the exact same way as Wigner himself). To see Wigner's classification explicitly, you probably should check out the following[E.P. Wigner, Ann. Math., 40, 149, (1939)].