On a super-analog of the Schur-Weyl Duality

2022/08/15 by Borodin, Alexei, Rozhkovskaya, Natasha
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2208.07434

Abstract

Two super-analogs of the Schur-Weyl duality are considered: the duality of actions in (ℂ^m|n)^{⊗ N} of the Lie superalgebra \mathfrakgl(m,n) and the symmetric group S_N, and the duality of actions of the Lie superalgebra Q(n) and a certain finite group Se(N) in (ℂ^n|n)^{⊗ N}. We construct an isomorphism of symmetric and universal enveloping algebras of these Lie superalgebras called special symmetrization. Using this isomorphism of vector spaces we describe explicitly the duality between the centers of the corresponding universal enveloping algebras and the group algebras.

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