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M. Srednicki says in the book "Quantum Field Theory" on page 211 that:
I would really appreciate if someone could introduce me a good reference for understanding the irreducible decomposition of representations like $2\otimes 2=1_A \oplus 3_S$. Where can I find and learn them well?
$\begingroup$Here, but you learned about it in basic QM addition of spins: you are simply writing it in representation dimensionality formulas, instead of spin...$\endgroup$