A general approach to constructing minimal representations of Lie 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.