Generalized Representation Stability and FId-modules
Abstract
In this note we consider the complex representation theory of FId, a natural generalization of the category FI of finite sets and injections. We prove that finitely generated FId-modules exhibit behaviors in the spirit of Church-Farb representation stability theory, generalizing a theorem of Church, Ellenberg, and Farb which connects finite generation of FI-modules to representation stability.
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