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On computing the eventual behavior of an $\mathrm {FI}$-module over the rational numbers


Author: John D. Wiltshire-Gordon
Journal: Math. Comp. 89 (2020), 2985-3001
MSC (2010): Primary 18A25; Secondary 16G10
DOI: https://doi.org/10.1090/mcom/3538
Published electronically: June 1, 2020
MathSciNet review: 4136554
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Abstract: We give a formula for the eventual multiplicities of irreducible representations appearing in a finitely presented $\mathrm {FI}$-module over the rational numbers. The result relies on structure theory due to Sam–Snowden [Trans. Amer. Math. Soc. 146 (2018), no. 10, pp. 4117-4126].


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Additional Information

John D. Wiltshire-Gordon
Affiliation: Department of Mathematics, Van Vleck Hall, University of Wisconsin-Madison 480 Lincoln Drive, Madison, Wisconsin 53706
MR Author ID: 1017529
Email: jwiltshiregordon@gmail.com

Keywords: FI-modules
Received by editor(s): May 8, 2019
Received by editor(s) in revised form: January 27, 2020
Published electronically: June 1, 2020
Additional Notes: The author acknowledges support from the NSF through grant DMS-1502553.
Article copyright: © Copyright 2020 American Mathematical Society