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I have a question that will probably turn out to be trivial. I have the following matrix:

$$

U=\text{diag}(e^{2i\alpha},e^{-i\alpha},e^{-i\alpha}).

$$

This seems to me as an SU(2) matrix in the adjoint representation since it's unitary and has determinant 1. Am I right?

If so, for a small value of [itex]\alpha[/itex] from what combination of the generators can I obtain it?

Thanks!

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# A particular SU(2) matrix

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