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

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- by Christopher Ryba PDF
- Represent. Theory
**24**(2020), 229-234 Request permission

## 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).## 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
- © Copyright 2020 American Mathematical Society
- Journal: Represent. Theory
**24**(2020), 229-234 - MSC (2010): Primary 05E10, 20C30
- DOI: https://doi.org/10.1090/ert/540
- MathSciNet review: 4127906