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Let $V$ be somecomplex irreducible representation of $SU\left(N\right)$. I read that to compute the Dynkin labels of the weights, one can take the highest weight and then subtract from it the rows of the Cartan matrix. This makes sense, since weights of an irreducible representation must differ by roots.

My question is, which rows of the Cartan are the correct ones to use? For instance, for $SU\left(5\right)$, suppose the highest weight is $\left(0,0,0,1\right)$. I know the Cartan matrix is

$$\left(\begin{array}{cccc} 2 & -1\\ -1 & 2 & -1\\ & -1 & 2 & -1\\ & & -1 & 2 \end{array}\right)$$ Which rows do I subtract from the highest weight Dynkin label to obtain the other Dynkin labels, and when do I stop?

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