Semisimplification functors give explicit, global, categorical-action-compatible equivalences between certain subcategories of modular representations of symmetric groups S_n and S_{n-p^r}.
Stability and periodicity in the modular representation theory of symmetric groups
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abstract
We study asymptotic properties of the modular representation theory of symmetric groups and investigate modular analogs of stabilization phenomena in characteristic zero. The main results are equivalences of categories between certain abelian subcategories of representations of $S_n$ and $S_m$ for different $n$ and $m$. We apply these results to obtain a structural result for $FI$-modules, and to prove a result conjectured by Deligne in a recent letter to Ostrik.
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Semisimplifying categorical Heisenberg actions and periodic equivalences
Semisimplification functors give explicit, global, categorical-action-compatible equivalences between certain subcategories of modular representations of symmetric groups S_n and S_{n-p^r}.