On the tails of FI-modules
Representation Theory
2019-09-24 v1 Algebraic Topology
Combinatorics
Abstract
We study the end-behavior of integer-valued FI-modules. Our first result describes the high degrees of an FI-module in terms of newly defined tail invariants. Our main result provides an equivalence of categories between FI-tails and finitely supported modules for a new category that we call FJ. Objects of FJ are natural numbers, and morphisms are infinite series with summands drawn from certain modules of Lie brackets.
Keywords
Cite
@article{arxiv.1909.09729,
title = {On the tails of FI-modules},
author = {Peter Patzt and John D. Wiltshire-Gordon},
journal= {arXiv preprint arXiv:1909.09729},
year = {2019}
}
Comments
32 pages