Stability and periodicity in the modular representation theory of symmetric groups

Nate Harman

Stability and periodicity in the modular representation theory of symmetric groups

Representation Theory 2016-10-04 v3

Authors: Nate Harman

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.

Keywords

modular representation theory symmetric group stability periodicity category equivalence FI-module Deligne conjecture

Cite

@article{arxiv.1509.06414,
  title  = {Stability and periodicity in the modular representation theory of symmetric groups},
  author = {Nate Harman},
  journal= {arXiv preprint arXiv:1509.06414},
  year   = {2016}
}

Comments

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

Stability and periodicity in the modular representation theory of symmetric groups

Abstract

Keywords

Cite

Comments

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