Lie supergroups, unitary representations, and invariant cones

TL;DR

This paper explores the application of invariant convex cones in Lie algebras to analyze unitary representations of Lie supergroups, including recent classification results for nilpotent cases using coadjoint orbit methods.

Contribution

It introduces a novel approach connecting invariant convex cones with the classification of unitary representations of Lie supergroups, expanding the theoretical framework.

Findings

Application of invariant convex cones to Lie supergroups

Classification of irreducible unitary representations of nilpotent Lie supergroups

Use of coadjoint orbit method for representation classification

Abstract

The main result of this article is an application of the theory of invariant convex cones of Lie algebras to the study of unitary representations of Lie supergroups. It also includes an exposition of recent results of the second author on the classification of irreducible unitary representations of nilpotent Lie supergroups using the method of coadjoint orbits.