Schur--Weyl Equivalences for Wreath Product Superalgebras

2025/09/23 by Grimley, Lauren, Kujawa, Jonathan R.
#16G99. Secondary 20B30 #FOS: Mathematics #Primary 17B10 #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2509.18598

Abstract

Let A be an associative superalgebra over a field of characteristic zero. Let n ≥ d+1. The main result of the paper establishes an equivalence of categories between supermodules for the wreath product S_d \wr A and an explicitly defined category of supermodules for the general linear Lie algebra \mathfrakgl_n(A). We also give an example showing the bound n ≥ d+1 cannot be improved.

Citations

• Quantum wreath products and Schur-Weyl duality I
• Turner doubles and generalized Schur algebras
• Integral Bases for the Universal Enveloping Superalgebras of Map Superalgebras II
• Classification of finite-growth general Kac-Moody superalgebras

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• Representation type of Schur superalgebras
• Polynomial super representations of the hyperalgebra of \mathfrakgl_m|n at roots of unity
• Lie Superautomorphisms on Associative Algebras, II
• On a super-analog of the Schur-Weyl Duality