2 problems

Let $F$ be a field of characteristic $p>0$, let $\ell\in\mathbb{N}$, and let $\xi=(p^{\ell-1},\ldots,p^{\ell-1})\vDash p^\ell$. Let $\operatorname{Lie}(p^\ell)$, $e_{(p^\ell),F}$,…

Let $F$ be an algebraically closed field of characteristic $p>0$, and for each $n obreakgeqslant 2$ let $mathrm{Lie}F(n)$ be the Lie module of the symmetric group $mathfrak{S}n$. W…