Littlewood complexes for symmetric groups

Author:
Christopher Ryba

Journal:
Represent. Theory **25** (2021), 594-605

MSC (2020):
Primary 20C30, 20C32

DOI:
https://doi.org/10.1090/ert/575

Published electronically:
July 13, 2021

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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

Email:
ryba@math.berkeley.edu

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