## A basic question on representation theory

1. The problem statement, all variables and given/known data

Hey, this is problem 4A out of Georgi (Lie Algebras in particle physics). The question says given an operator $$O_x$$ , x=1,2, in the spin 1/2 rep of SU(2). $$[J_a,O_x]=O_y(\sigma_a)_{yx}/2$$ where $$\sigma_a$$ are the Pauli spin matrices.

Given
$$A=\langle 3/2, -1/2, \alpha|O_1|1,-1,\beta\rangle$$
find

$$B=\langle 3/2, -3/2, \alpha|O_2|1,-1,\beta\rangle$$

2. Relevant equations

This seems to be a basic application of the Wigner Eckart theorem, I just cannot seem to make any fruitful progress. Any comments/ hints would be appreciated.

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