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FI$^m$-modules over Noetherian rings

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arxiv 1705.00876 v2 pith:353JMIJB submitted 2017-05-02 math.RT math.ATmath.KTmath.RA

Liping Li , Nina Yu This is my paper · ORCID
classification math.RTmath.ATmath.KTmath.RA
keywords categorymodulesrepresentationcharacteristiccopiesfieldsfinitelygadish
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abstract

In this paper we study representation theory of the category FI$^m$ introduced by Gadish which is a product of copies of the category FI, and show that quite a few interesting representational and homological properties of FI can be generalized to FI$^m$ in a natural way. In particular, we prove the representation stability property of finitely generated FI$^m$-modules over fields of characteristic 0.

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