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arXiv · 2410.04902

Unitary branching rules for the general linear Lie superalgebra

Mark Gould·Yang Zhang
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Abstract

In terms of highest weights, we establish branching rules for finite dimensional unitary simple modules of the general linear Lie superalgebra $\mathfrak{gl}_{m|n}$. Our proof uses the Howe duality for $\mathfrak{gl}_{m|n}$, as well as branching rules for Kac modules. Moreover, we derive the branching rules of type 2 unitary simple $\mathfrak{gl}_{m|n}$-modules, which are dual to the aforementioned unitary modules.

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Mark Gould, Yang Zhang. 2024-10-07. Unitary branching rules for the general linear Lie superalgebra. https://arxiv.org/abs/2410.04902

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