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arXiv · 2310.04661

Integrable systems on rectangular $\mathcal{W}$-superalgebras via super Adler-type operators

Sylvain Carpentier·Gahng Sahn Lee·Uhi Rinn Suh
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Abstract

In this paper, we introduce a class of super Adler-type operators associated with the Lie superalgebra $\mathfrak{gl}(m|n)$. We show that these operators generate Poisson vertex superalgebras which are isomorphic to the classical $\mathcal{W}$-superalgebras associated with $\mathfrak{gl}(m|n)$ and some rectangular nilpotent elements. We use this isomorphism to construct integrable hierarchies on these rectangular $\mathcal{W}$-superalgebras.

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Sylvain Carpentier, Gahng Sahn Lee, Uhi Rinn Suh. 2023-10-07. Integrable systems on rectangular $\mathcal{W}$-superalgebras via super Adler-type operators. https://arxiv.org/abs/2310.04661

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