Use the ( mathrm SU (3) ) algebra to prove that (T pm , V pm ), and (U pm )have the raising and lowering properties in the ( left(T 3 , Y ight) ) plane that we have ascribed to them Prove that the allowed values of (Y ) and (T 3 ) are indicated by the dots shown in the following diagram but that th...

Use the (mathrm{SU}(3)) algebra to prove that (T_{ pm}, V_{ pm}), and (U_{ pm})have the raising and

Question:

Use the $\mathrm{SU}(3)$ algebra to prove that $T_{ \pm}, V_{ \pm}$, and $U_{ \pm}$have the raising and lowering properties in the $\left(T_{3}, Y\right)$ plane that we have ascribed to them. Prove that the allowed values of $Y$ and $T_{3}$ are indicated by the dots shown in the following diagram

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but that the basic principles of representation theory require that the possible occupied sites in the SU(3) irreps be further restricted to those marked by a heavy dot in the following diagram.

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