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.
Modular Representation Theory of Symmetric Groups
The complexities of some simple modules of the symmetric groups
On a relation between certain character values of symmetric groups and its connection with creation operators of symmetric functions
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