We give refined bounds for the regularity of FI-modules and the stable ranges of FI-modules for various forms of their stabilization studied in the representation stability literature. We show that our bounds are sharp in several cases. We apply these to get explicit stable ranges for diagonal coinvariant algebras, and improve those for ordered configuration spaces of manifolds and congruence subgroups of general linear groups.
Bounding the homology of FI-modules
Distinction and Asai $L$-functions for generic representations of general linear groups over p-adic fields
Cohomology at infinity and the well-rounded retract for general Linear Groups
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