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

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John D. Wiltshire-Gordon
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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].## References

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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
- 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.
- © Copyright 2020 American Mathematical Society
- Journal: Math. Comp.
**89**(2020), 2985-3001 - MSC (2010): Primary 18A25; Secondary 16G10
- DOI: https://doi.org/10.1090/mcom/3538
- MathSciNet review: 4136554