Measurability of open orbits in flag supermanifolds

TL;DR

This paper extends the concept of measurability of open orbits from classical flag manifolds to the supersymmetric setting, providing a classification of measurable open orbits in flag supermanifolds.

Contribution

It generalizes the notion of measurability to supermanifolds and classifies all measurable open orbits in flag supermanifolds.

Findings

Measurability in supermanifolds is characterized by invariant volume elements.

A complete classification of measurable open orbits in flag supermanifolds is provided.

The results extend classical orbit measurability to the supersymmetric context.

Abstract

Let $G_\mathbb{R}$ be a Lie group and $G$ its complexification. An open $G_\mathbb{R}$-orbit in a $G$-flag manifold is measurable whenever it carries a $G_\mathbb{R}$-invariant volume element. In this paper the notion of measurability is generalized to the supersymmetric setting and a classification of measurable open orbits in flag supermanifolds is given.