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Representation Stability

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arxiv 1404.4065 v1 pith:UPDV7PTQ submitted 2014-04-15 math.GT math.ATmath.RT

Benson Farb This is my paper · ORCID
classification math.GTmath.ATmath.RT
keywords representationphenomenonstabilitytheorybehindcertaindescribeexplains
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Representation stability in the (co)homology of vertical configuration spaces

    math.AT 2024-12 accept novelty 6.0 of 10

    The (co)homology of vertical configuration spaces is representation stable as S_k≀S_n-representations, with explicit stable ranges and an improved homological stability range for the unordered spaces.

  2. Lie algebras and the (co)homology of configuration spaces

    math.AT 2024-12 unverdicted novelty 1.0 of 10

    A survey that organizes decades of results connecting configuration space (co)homology to Lie algebra (co)homology into three perspectives: partitions, commutativity, and Poincaré duality.

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