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15 September 2017 Representation stability and finite linear groups
Andrew Putman, Steven V Sam
Duke Math. J. 166(13): 2521-2598 (15 September 2017). DOI: 10.1215/00127094-2017-0008

Abstract

We study 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 we prove basic structural properties such as local 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.

Citation

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Andrew Putman. Steven V Sam. "Representation stability and finite linear groups." Duke Math. J. 166 (13) 2521 - 2598, 15 September 2017. https://doi.org/10.1215/00127094-2017-0008

Information

Received: 20 December 2015; Revised: 13 January 2017; Published: 15 September 2017
First available in Project Euclid: 20 June 2017

zbMATH: 06797413
MathSciNet: MR3703435
Digital Object Identifier: 10.1215/00127094-2017-0008

Subjects:
Primary: 18A25
Secondary: 11F75, 20C33

Rights: Copyright © 2017 Duke University Press

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Vol.166 • No. 13 • 15 September 2017
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