Representation Stability
Benson Farb
TL;DR
This paper introduces the concept of representation stability, explaining how sequences of spaces stabilize in structure through the lens of FI-modules in representation theory.
Contribution
It presents a framework based on FI-modules that explains the underlying mechanism of representation stability.
Findings
Sequences of spaces exhibit stable structure when analyzed via representation theory.
The FI-module framework provides a systematic explanation for this stability.
The paper sketches the theoretical basis for understanding representation stability.
Abstract
Representation stability is a phenomenon whereby the structure of certain sequences of spaces can be seen to stabilize when viewed through the lens of representation theory. In this paper I describe this phenomenon and sketch a framework, the theory of FI-modules, that explains the mechanism behind it.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Topological and Geometric Data Analysis · Geometric and Algebraic Topology