Stability and periodicity in the modular representation theory of symmetric groups

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.

Removed a unnecessary restriction on characteristic. Fixed some few minor errors and clarified the exposition in places

References in corpus (2)

• FI-modules and stability for representations of symmetric groups
• FI-modules over Noetherian rings

Cited by in corpus (5)

• Periodicity in the cohomology of symmetric groups via divided powers
• Deligne categories as limits in rank and characteristic
• Lectures on Symmetric Tensor Categories
• On stability and nonvanishing of homomorphism spaces between Weyl modules
• Asymptotic behaviors of representations of graded categories with inductive functors