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arXiv · 1504.07675

On central stability

Wee Liang Gan·Liping Li
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Abstract

The notion of central stability was first formulated for sequences of representations of the symmetric groups by Putman. A categorical reformulation was subsequently given by Church, Ellenberg, Farb, and Nagpal using the notion of FI-modules, where FI is the category of finite sets and injective maps. We extend the notion of central stability from FI to a wide class of categories, and prove that a module is presented in finite degrees if and only if it is centrally stable. We also introduce the notion of $d$-step central stability, and prove that if the ideal of relations of a category is generated in degrees at most $d$, then every module presented in finite degrees is $d$-step centrally stable.

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Wee Liang Gan, Liping Li. 2015-04-28. On central stability. https://arxiv.org/abs/1504.07675

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