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 $SU(3) \times U(1)$ using the inverse of the Cartan matrix of $SU(4)$ and the weight scheme?