Automorphism groups of some Mordell–Weil lattices

The automorphism groups $G=\operatorname{Aut}(\Lambda)$ are calculated for the Mordell–Weil lattices connected with globally irreducible representations of the simple groups $S=\operatorname{PSL}(2,p)$ ($p$ a prime, $p\equiv 3$ $(\operatorname{mod}4)$) and $S=\operatorname{PSU}(3,q)$ $(q=p^f>2)$ of degree $p-1$ and $2q(q-1)$, respectively. In particular, it is shown that in the great majority of cases $S$ is the unique nonabelian composition factor of $G$.