Representation stability and finite linear groups
By Andrew Putman, Steven V. Sam. 2014
133 citations recorded by the source corpus.
We construct analogues of FI-modules where the role of the symmetric group is played by the general linear groups and the symplectic groups over finite rings and prove basic structural properties such as Noetherianity. Applications include a proof of the Lannes--Schwartz Artinian conjecture in the generic representation theory of finite fields, very general homological stability theorems with twisted coefficients for the general linear and symplectic groups over finite rings, and representation-theoretic versions of homological stability for congruence subgroups of the general linear group, the automorphism group of a free group, the symplectic group, and the mapping class group.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/28b31da6580baf71231bda64eb150c3c0898c289
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In Algebra and Number Theory
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In Mathematical Physics
Citations in the corpus
- FI-modules and the cohomology of modular representations of symmetric groups (2015, background): “include: cohomology of free groups via polynomial functors [DPV]; rational cohomology of classical groups via polynomial functors [To], [Ku]; homology groups Ht(GLn(R), T(Adn(R)) where T : Z-Mod → Z-Mod is a functor of finite degree [Dw]; homology groups Ht(Sn,Vn) where V is a finitely generated FI-”