Representation stability and finite linear groups
Algebraic Topology
2017-10-18 v3 Group Theory
Geometric Topology
Representation Theory
Abstract
We construct analogues of FI-modules where the role of the symmetric group is played by the general linear groups and the symplectic groups over finite rings and prove basic structural properties such as Noetherianity. Applications include a proof of the Lannes--Schwartz Artinian conjecture in the generic representation theory of finite fields, very general homological stability theorems with twisted coefficients for the general linear and symplectic groups over finite rings, and representation-theoretic versions of homological stability for congruence subgroups of the general linear group, the automorphism group of a free group, the symplectic group, and the mapping class group.
Cite
@article{arxiv.1408.3694,
title = {Representation stability and finite linear groups},
author = {Andrew Putman and Steven V Sam},
journal= {arXiv preprint arXiv:1408.3694},
year = {2017}
}
Comments
53 pages, 5 figures; major revision; to appear in Duke Math J