# The representation $\Phi_{n}$ of $SU_{2}$ is irreducible.

The proof is given below:

But I do not understand why " we first determine which of the spaces of $$V_{n}$$ are invariant under T " as he said in the second sentence. could anyone explain this for me please?

$$A(z) = \begin{bmatrix} z & 0 \\ 0 & z^{-1} \end{bmatrix}$$

And $$z \in \mathbb{C}.$$

This link describes what is $$\Phi_{n}$$: