English

Minimal representations of the metaplectic Lie supergroup and the super Segal-Bargmann transform

Representation Theory 2023-09-19 v1

Abstract

We construct a Schr\"odinger model and a Fock model of a minimal representation of the metaplectic Lie supergroup Mp(2m2n,2n)\mathrm{Mp}(2m|2n,2n). Then, we show that the Schr\"odinger model of the minimal representation leads to an already known Schr\"odinger model of the metaplectic representation of Mp(2m2n,2n)\mathrm{Mp}(2m|2n,2n). Therefore, the Fock model of the minimal representation allows us to construct a Fock model of this metaplectic representation. We then construct an intertwining super Segal-Bargmann transform which extends the classical Segal-Bargmann transform.

Keywords

Cite

@article{arxiv.2309.09693,
  title  = {Minimal representations of the metaplectic Lie supergroup and the super Segal-Bargmann transform},
  author = {Sam Claerebout},
  journal= {arXiv preprint arXiv:2309.09693},
  year   = {2023}
}