Super K\"ahler structures on the complex Abelian Lie supergroups
Differential Geometry
2024-08-27 v2
Abstract
We consider a real Abelian Lie supergroup acting on its complexification , equipped with a -invariant super K\"ahler form. We extend the scheme of classical geometric quantization to this setting and construct a unitary -representation. We show that the occurrences of its irreducible subrepresentations are governed by the image of the moment map of the super K\"ahler form. As an application, we construct a Gelfand model of , namely a unitary -representation in which every unitary irreducible representation occurs exactly once.
Cite
@article{arxiv.2312.00444,
title = {Super K\"ahler structures on the complex Abelian Lie supergroups},
author = {Meng-Kiat Chuah and Fabio Gavarini},
journal= {arXiv preprint arXiv:2312.00444},
year = {2024}
}
Comments
28 pages - Submitted. W.r.t. the previous version, the main core of the content stays the same, yet the paper has been entirely re-written, with several improvements here and there