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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
Published electronically: June 25, 2020
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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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Christopher Ryba
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

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