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Generalized Representation Stability and FI_d-modules

Published 8 Jun 2016 in math.RT, math.AT, and math.CO | (1606.02673v4)

Abstract: In this note we consider the complex representation theory of FI_d, a natural generalization of the category FI of finite sets and injections. We prove that finitely generated FI_d-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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