Polynomial conditions and homology of FI-modules
K-Theory and Homology
2023-08-21 v6 Group Theory
Representation Theory
Abstract
We identify two recursively defined polynomial conditions for FI-modules in the literature. We characterize these conditions using homological invariants of FI-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
Cite
@article{arxiv.2209.10496,
title = {Polynomial conditions and homology of FI-modules},
author = {Cihan Bahran},
journal= {arXiv preprint arXiv:2209.10496},
year = {2023}
}
Comments
21 pages. To appear in Pacific Journal of Mathematics