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## Main Question or Discussion Point

I'm solving these problems concerning the SU(4) group and I've reached the point where I have determined the Cartan matrix of SU(4), its inverse and the weight schemes for (1 0 0) and (0 1 0) highest weight states.

How do I decompose the (1 0 0) and (0 1 0) into irreps of SU(3) x U(1) using the inverse of the Cartan matrix of SU(4) and the weight scheme?

How do I decompose the (1 0 0) and (0 1 0) into irreps of SU(3) x U(1) using the inverse of the Cartan matrix of SU(4) and the weight scheme?