On modular representations of semigroups $S_p\times T_p$

Let $p$ be simple, and let $S_p$ and $T_p$ be the symmetric group and the symmetric semigroup of degree $p$, respectively. The theorem of this paper says that the direct product $S_p\times T_p$ are of wild representation type over any field of characteristic $p$. The main case is $p=2$.