Littlewood Complexes for Symmetric Groups

DOI10.1090/ERT/575arXiv2004.00183MaRDI QIDQ6337825

Christopher Ryba

Publication date: 31 March 2020

Abstract: We construct a complex $$ resolving the irreducible representations $mathcal{S}^{lambda[n]}$ of the symmetric groups $S_n$ by representations restricted from $G{L}_n(k)$. This construction lifts to $mathrmRep(S_{i}nfty)$, where it yields injective resolutions of simple objects. It categorifies stable Specht polynomials, and allows us to understand evaluations of these polynomials for all $n$.

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Representation theory for linear algebraic groups (20G05) Representations of infinite symmetric groups (20C32)

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