Littlewood Complexes for Symmetric Groups

2020/04/01 by Ryba, Christopher
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2004.00183

Abstract

We construct a complex L_\bullet^λ resolving the irreducible representations S^λ[n] of the symmetric groups S_n by representations restricted from GL_n(k). This construction lifts to Rep(S_∞), 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.

Related

• Stable Higher Specht Polynomials and Representations of Infinite Symmetric Groups
• Wreath Generalization of Littlewood Reciprocity
• Generalized Higher Specht Polynomials and Homogeneous Representations of Symmetric Groups
• Resolving Irreducible ℂS_n-Modules by Modules Restricted from GL_n(ℂ)
• Multiplication of polynomials on Hermitian symmetric spaces and Littlewood-Richardson coefficients