An explicit embedding of the Tits group in the compact real form of $E_6$ (1208.4221v1)

Abstract: We construct a set of $27\times 27$ unitary matrices which give an explicit embedding of the Tits group in the compact real form of the Lie group of type $E_6$. A subset gives an embedding of $\mathrm{PSL}_2(25)$ in $F_4$.