An inductive machinery for representations of categories with shift functors

Wee Liang Gan Liping Li

K-Theory and Homology Representation Theory Rings and Algebras mathscidoc:1702.20004

We describe an inductive machinery to prove various properties of representations of a category equipped with a generic shift functor. Specifically, we show that if a property (P) of representations of the category behaves well under the generic shift functor, then all finitely generated representations of the category have the property (P). In this way, we obtain simple criteria for properties such as Noetherianity, finiteness of Castelnuovo-Mumford regularity, and polynomial growth of dimension to hold. This gives a systemetic and uniform proof of such properties for representations of the categories $\FI_G$ and $\OI_G$ which appear in representation stability theory.
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@inproceedings{weean,
  title={An inductive machinery for representations of categories with shift functors},
  author={Wee Liang Gan, and Liping Li},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170222110723151462507},
}
Wee Liang Gan, and Liping Li. An inductive machinery for representations of categories with shift functors. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170222110723151462507.
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