Generalized representation stability and FId -modules

Eric Ramos

doi:10.1090/proc/13618

Generalized representation stability and FI_d -modules

Eric Ramos

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

In this note we consider the complex representation theory of FI_d, a natural generalization of the category FI of finite sets and injections. We prove that finitely generated 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 FI-modules to representation stability.

Original language	English
Pages (from-to)	4647-4660
Number of pages	14
Journal	Proceedings of the American Mathematical Society
Volume	145
Issue number	11
DOIs	https://doi.org/10.1090/proc/13618
State	Published - 2017

Keywords

FI-modules
Representation stability

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10.1090/proc/13618

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title = "Generalized representation stability and FId -modules",

abstract = "In this note we consider the complex representation theory of FId, a natural generalization of the category FI of finite sets and injections. We prove that finitely generated FId -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 FI-modules to representation stability.",

keywords = "FI-modules, Representation stability",

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note = "Publisher Copyright: {\textcopyright} 2017 American Mathematical Society.",

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doi = "10.1090/proc/13618",

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pages = "4647--4660",

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T1 - Generalized representation stability and FId -modules

AU - Ramos, Eric

PY - 2017

Y1 - 2017

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AB - In this note we consider the complex representation theory of FId, a natural generalization of the category FI of finite sets and injections. We prove that finitely generated FId -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 FI-modules to representation stability.

KW - FI-modules

KW - Representation stability

UR - https://www.scopus.com/pages/publications/85029605685

UR - https://www.scopus.com/pages/publications/85029605685#tab=citedBy

U2 - 10.1090/proc/13618

DO - 10.1090/proc/13618

M3 - Article

AN - SCOPUS:85029605685

SN - 0002-9939

VL - 145

SP - 4647

EP - 4660

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 11

ER -

Generalized representation stability and FI_d -modules

Abstract

Keywords

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