On central stability

Wee Liang Gan Liping Li

Representation Theory Rings and Algebras mathscidoc:1702.02012

to appear in Bull. Lond. Math. Soc., 2017
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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  title={On central stability},
  author={Wee Liang Gan, and Liping Li},
  booktitle={to appear in Bull. Lond. Math. Soc.},
Wee Liang Gan, and Liping Li. On central stability. 2017. In to appear in Bull. Lond. Math. Soc.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170222105938692158503.
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