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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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