# A general approach to constructing minimal representations of Lie supergroups

## TL;DR

This paper develops a general method for constructing minimal representations of Lie supergroups derived from Jordan superalgebras, successfully applying it to specific cases like orthosymplectic and exceptional supergroups.

## Contribution

It introduces a unified approach to minimal representations of Lie supergroups via the TKK construction, extending existing methods to the super setting.

## Key findings

- Constructed Fock, Schrödinger, and Segal-Bargmann models for certain supergroups.
- Identified obstacles in applying the approach to periplectic and queer superalgebras.
- Demonstrated the approach's effectiveness for orthosymplectic and exceptional supergroups.

## Abstract

In this paper we describe an approach to generalise minimal representations to the super setting for Lie superalgebras obtained from Jordan superalgebras using the TKK construction. This approach was used successfully to construct a Fock model, a Schr\"odinger model and intertwining Segal-Bargmann transform for the orthosymplectic Lie supergroup $\mathop{OSp}(p,q|2n)$ and the exceptional Lie supergroup $\mathbb{D}(2,1;\alpha)$. We also describe some obstacles to use this approach for the periplectic and queer Lie superalgebras.