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arXiv · 2312.00444

Super K\"ahler structures on the complex Abelian Lie supergroups

Meng-Kiat Chuah·Fabio Gavarini
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Abstract

Let $G$ be a real Abelian Lie supergroup, let $M$ be its complexification. We classify the $G$-invariant super K\"ahler forms on $M$. For the super K\"ahler forms with Hamiltonian actions, we extend the scheme of geometric quantization to the super setting and construct unitary $G$-representations. We show that the irreducible representations that occur in these unitary representations are governed by the image of the moment maps of super K\"ahler forms. As an application, we construct a Gelfand model of $G$, namely a unitary $G$-representation in which every unitary irreducible representation occurs exactly once.

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Meng-Kiat Chuah, Fabio Gavarini. 2023-12-01. Super K\"ahler structures on the complex Abelian Lie supergroups. https://arxiv.org/abs/2312.00444

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