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arXiv · 2603.07541

Representations of shifted super Yangians and finite $W$-superalgebras of type A

Kang Lu·Yung-Ning Peng
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Abstract

In this article, we study the representation theory of shifted super Yangians and finite $W$-superalgebras of type A. A criterion for the finite dimensionality of irreducible modules is obtained in the standard parity case. Furthermore, we provide an explicit Gelfand-Tsetlin character formula for Verma modules of finite $W$-superalgebras. As an application, we show that the centers of the finite $W$-superalgebras associated to any even nilpotent elements belonging to the same general linear Lie superalgebra are all isomorphic to the center of the universal enveloping superalgebra.

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BibTeXRIS

Kang Lu, Yung-Ning Peng. 2026-03-14. Representations of shifted super Yangians and finite $W$-superalgebras of type A. https://arxiv.org/abs/2603.07541

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