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 . 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 . 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}
}