Realization of irreducible unitary representations of $ \mathfrak{osp}(M/N; \mathbb{R}) $ on Fock spaces

TL;DR

This paper classifies irreducible super unitary representations of the orthosymplectic Lie superalgebra using super dual pairs, advancing the understanding of their structure on Fock spaces.

Contribution

It introduces a classification method for irreducible super unitary representations of $rak{osp}(M/N; R)$ via super dual pairs, providing new insights into their realization on Fock spaces.

Findings

Complete classification of irreducible super unitary representations

Utilization of super dual pairs in the classification process

Representation realization on Fock spaces

Abstract

We classify irreducible super unitary representations of an orthosymplectic Lie superalgebra $ \mathfrak{osp}(M/N; \mathbb{R} ) $ using the notion of super dual pairs in $ \mathfrak{osp}(M/N) $.