Find the relationship of the eight SU(3) operators \(T_{ \pm}, V_{ \pm}, U_{ \pm}, T_{3}\), and \(Y\) defined in Eqs. (8.2) and (8.7)-(8.8), and the nine oscillator operators \(\left(A_{i}^{j}\right)_{k l} \equiv \delta_{i k} \delta_{j l}-\frac{1}{3} \delta_{k l}\), with a constraint \(A_{1}^{1}+A_{2}^{2}+A_{3}^{3}=0\).

Data from Eq. 8.2

Data from Eq. 8.7

Data from Eq. 8.8

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0 0 0 0 0 0 0 --619-3619 = 0 0 0 i 0 = 00 -2) 0 0 = 0 0 0 0 0 00 = 0 = 00 1:9 16:9 6:9- 0 00 0 0 0 0 00 00 1 0 0 -i 1 0 1 12 = i 0 0 13 = 0 -1 0 0 0 =