Representation Stability

Abstract

Representation stability is a phenomenon whereby the structure of certain sequences $X_n$ 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.

Contribution to Proceedings of the ICM 2014, Seoul

References in corpus (3)

• Representation theory and homological stability
• Homological stability for configuration spaces of manifolds
• Homological stability for unordered configuration spaces

Cited by in corpus (13)

• Representation stability and finite linear groups
• FI-modules and the cohomology of modular representations of symmetric groups
• Noetherian property of infinite EI categories
• Categories of FI type: a unified approach to generalizing representation stability and character polynomials
• The homology of the Higman-Thompson groups
• Filtrations and Homological degrees of FI-modules
• Koszulity of directed categories in representation stability theory
• Twisted cohomology of configuration spaces and spaces of maximal tori via point-counting
• Coinduction functor in representation stability theory
• Polynomial splitting measures and cohomology of the pure braid group
• Structures in representation stability
• A Survey of Representation Stability Theory
• On chromatic functors and stable partitions of graphs