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Representation Theory

ISSN 1088-4165



Littlewood complexes for symmetric groups

Author: Christopher Ryba
Journal: Represent. Theory 25 (2021), 594-605
MSC (2020): Primary 20C30, 20C32
Published electronically: July 13, 2021
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Abstract: We construct a complex $\mathcal {L}_\bullet ^\lambda$ resolving the irreducible representations $\mathcal {S}^{\lambda [n]}$ of the symmetric groups $S_n$ by representations restricted from $GL_n(k)$. This construction lifts to $\mathrm {Rep}(S_\infty )$, where it yields injective resolutions of simple objects. It categorifies stable Specht polynomials, and allows us to understand evaluations of these polynomials for all $n$.

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Additional Information

Christopher Ryba
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
MR Author ID: 1317998
ORCID: 0000-0002-8114-8263

Received by editor(s): May 28, 2020
Received by editor(s) in revised form: March 2, 2021
Published electronically: July 13, 2021
Article copyright: © Copyright 2021 American Mathematical Society