Coadjoint orbits of the odd real symplectic group

TL;DR

This paper classifies all coadjoint orbits of the odd real symplectic group by providing explicit representatives, extending methods used for the Poincaré group with novel details.

Contribution

It offers a complete description of coadjoint orbits for the odd real symplectic group, a previously less understood class of Lie groups.

Findings

Explicit representatives for all coadjoint orbits provided

Method adapted from Poincaré group analysis with new details

Enhances understanding of the group's geometric and algebraic structure

Abstract

We give a representative of every coadjoint orbit of the odd symplectic group. Our argument follows that used for the Poincar\`{e} group but the details differ.