$p$-filtrations of dual Weyl modules

Abstract

Let $G$ be a semisimple algebraic group over a field of characteristic $p>0$. We prove that the dual Weyl modules for $G$ all have $p$-filtrations when $p$ is not too small. Moreover, we give applications of this theorem to $p^n$-filtrations for $n>1$, to modules containing the Steinberg module as a tensor factor, and to the Donkin conjecture on modules having $p$-filtrations.

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