GL-equivariant modules over polynomial rings in infinitely many variables

Our work is motivated by recent papers in the literature which study finiteness properties of infinite polynomial rings equipped with group actions. (For example, the paper by Church, Ellenberg and Farb on the category of FI-modules, which is equivalent to our category.) Along the way, we see severa...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2016-02, Vol.368 (2), p.1097-1158
Main Authors: Sam, Steven V, Snowden, Andrew
Format: Article
Language:English
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Summary:Our work is motivated by recent papers in the literature which study finiteness properties of infinite polynomial rings equipped with group actions. (For example, the paper by Church, Ellenberg and Farb on the category of FI-modules, which is equivalent to our category.) Along the way, we see several connections with the character polynomials from the representation theory of the symmetric groups. Several examples are given to illustrate that the invariants we introduce are explicit and computable.]]>
ISSN:0002-9947
1088-6850
DOI:10.1090/tran/6355