Consider the exceptional Lie group $F_4$. I want to represent this group in terms of matrices. In particular, I am interested in a maximal torus.
The first non-trivial representation of this group is $26$-dimensional, and the Cartan sub-algebra is $4$-dimensional. Therefore, the maximal torus is generated by four $26\times26$ matrices. Is the explicit form of these matrices available somewhere? Or how can I construct it myself?