## Generalized representation stability and $\mathrm {FI}_d$-modules

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- by Eric Ramos PDF
- Proc. Amer. Math. Soc.
**145**(2017), 4647-4660 Request permission

## Abstract:

In this note we consider the complex representation theory of $\mathrm {FI}_d$, a natural generalization of the category $\mathrm {FI}$ of finite sets and injections. We prove that finitely generated $\mathrm {FI}_d$-modules exhibit behaviors in the spirit of Church-Farb representation stability theory, generalizing a theorem of Church, Ellenberg, and Farb which connects finite generation of $\mathrm {FI}$-modules to representation stability.## References

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## Additional Information

**Eric Ramos**- Affiliation: Department of Mathematics, University of Wisconsin–Madison, Madison, Wisconsin 53706
- MR Author ID: 993563
- Email: eramos@math.wisc.edu
- Received by editor(s): November 11, 2016
- Received by editor(s) in revised form: December 5, 2016
- Published electronically: June 9, 2017
- Additional Notes: The author was supported by NSF grant DMS-1502553
- Communicated by: Jerzy Weyman
- © Copyright 2017 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**145**(2017), 4647-4660 - MSC (2010): Primary 05E10, 16G20, 18A25; Secondary 13D15
- DOI: https://doi.org/10.1090/proc/13618
- MathSciNet review: 3691984