The momentum map of the affine real symplectic group

TL;DR

This paper explores the relationship between the momentum map cocycle of the affine real symplectic group and coadjoint orbits of the odd real symplectic group, revealing new geometric insights.

Contribution

It establishes a connection between the momentum map cocycle and coadjoint orbits of the odd real symplectic group, introducing a novel geometric perspective.

Findings

The cocycle of the momentum map induces a coadjoint orbit with a modulus.

A new geometric interpretation of the affine symplectic group's action.

Linking the affine symplectic group to the odd real symplectic group's orbit structure.

Abstract

In this paper we explain how the cocycle of the momentum map of the action of the affine symplectic group on $\mathbb{R}^{2n}$ gives rise to a coadjoint orbit of the odd real symplectic group with a modulus.