Generalized Representation Stability and FI_d-modules

2016/06/08 by Eric Ramos, Ramos, Eric · 2 citations
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic, programming, and type systems #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1606.02673

openalex publication_date 2016/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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• Representation asymptotics in the homology of pure graph braid groups
• Representation stability for ordered Hurwitz spaces

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