A basic question on representation theory

nickthequick

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 [tex]O_x [/tex] , x=1,2, in the spin 1/2 rep of SU(2). [tex][J_a,O_x]=O_y(\sigma_a)_{yx}/2 [/tex] where [tex] \sigma_a[/tex] are the Pauli spin matrices.

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

[tex]
B=\langle 3/2, -3/2, \alpha|O_2|1,-1,\beta\rangle
[/tex]

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.