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Resolving irreducible $\mathbb {C}S_n$-modules by modules restricted from $GL_n(\mathbb {C})$


Author: Christopher Ryba
Journal: Represent. Theory 24 (2020), 229-234
MSC (2010): Primary 05E10, 20C30
DOI: https://doi.org/10.1090/ert/540
Published electronically: June 25, 2020
MathSciNet review: 4127906
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Abstract | References | Similar Articles | Additional Information

Abstract: We construct a resolution of irreducible complex representations of the symmetric group $S_n$ by restrictions of representations of $GL_n(\mathbb {C})$ (where $S_n$ is the subgroup of permutation matrices). This categorifies a recent result of Assaf and Speyer. Our construction also gives projective resolutions of simple $\mathcal {F}$-modules (here $\mathcal {F}$ is the category of finite sets).


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References
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Additional Information

Christopher Ryba
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
MR Author ID: 1317998
ORCID: 0000-0002-8114-8263
Email: ryba@mit.edu

Received by editor(s): January 4, 2019
Received by editor(s) in revised form: September 24, 2019
Published electronically: June 25, 2020
Article copyright: © Copyright 2020 American Mathematical Society