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I was trying to project out the two dimensional rep of S3 from its regular representation by using the projection operator (Georgi-Lie Algebras in Particle Physics-Chapter1).

Now, as we know, a two-dimensional representation occurs twice in a regular representation. Thus, I am able to project out a 4x4 matrix from the 6x6 matrix of regular representation. But I am not able to figure out a way to bring this 4x4 matrix into block diagonal form with two 2X2 matrices. Is there a general procedure to accomplish this?

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# Projecting out representations

Can you offer guidance or do you also need help?

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