Resolving irreducible ℂ𝕊_{𝕟}-modules by modules restricted from 𝔾𝕃_{𝕟}(ℂ)

Ryba, Christopher

doi:10.1090/ert/540

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

Represent. Theory 24 (2020), 229-234

DOI: https://doi.org/10.1090/ert/540

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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