Remote Access Representation Theory
Green Open Access

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
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 $n$.


References [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2020): 20C30, 20C32

Retrieve articles in all journals with MSC (2020): 20C30, 20C32


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