Abstract
|
|
We identify two recursively defined polynomial conditions for
-modules
in the literature. We characterize these conditions using homological invariants of
-modules
(namely the local degree and regularity, together with the stable degree) and clarify
their relationship. For one of these conditions, we give improved twisted
homological stability ranges for the symmetric groups. As another application, we
improve the representation stability ranges for congruence subgroups with
respect to the action of an appropriate linear group by a factor of 2 in its
slope.
|
Keywords
FI-modules, homological stability, representation
stability, congruence subgroups
|
Mathematical Subject Classification
Primary: 18A25, 20J06
Secondary: 11F75
|
Milestones
Received: 11 October 2022
Revised: 10 January 2023
Accepted: 10 January 2023
Published: 26 July 2023
|
| © 2023 MSP (Mathematical Sciences
Publishers). Distributed under the Creative Commons
Attribution License 4.0 (CC BY). |
Open Access made possible by participating
institutions via Subscribe to Open. 
|
