How calculate the cartan matrix of the twisted quantum affine algebras?

Question

the cartan matrix of the type $A_{2}^{(2)}$, $A_{2r-1}^{(2)}$, $A_{2r-1}^{(2)}$, $D_{r+1}^{(2)}$, $E_{6}^{(2)}$. I know the cartan matrix of the type $A_{2}^{(2)}$ is \begin{align} \left( \begin{array}{cc} 2 & -4 \\ -1 & 2 \\ \end{array} \right) \end{align}. But I don't know how calculate the cartan matrix of the rest types?

Answer 1

The Cartan matrices of these types are computed, among other references, in the book Affine Lie Algebras, Weight Multiplicities, and Branching Rules.

Remark: For the two-parameter case see the article Two-parameter twisted quantum affine algebras on page $4$.