Weighted nonlinear flag manifolds as coadjoint orbits

TL;DR

This paper explores the geometry of weighted nonlinear flag manifolds and their role as coadjoint orbits of Hamiltonian diffeomorphism groups, generalizing previous structures like Grassmannians.

Contribution

It introduces the concept of weighted nonlinear flags and demonstrates their use in describing coadjoint orbits in symplectic geometry.

Findings

Weighted nonlinear flags form a rich geometric structure.

These flags can be used to characterize coadjoint orbits of Hamiltonian diffeomorphisms.

The work generalizes the concept of weighted nonlinear Grassmannians.

Abstract

A weighted nonlinear flag is a nested set of closed submanifolds, each submanifold endowed with a volume density. We study the geometry of Frechet manifolds of weighted nonlinear flags, in this way generalizing the weighted nonlinear Grassmannians. When the ambient manifold is symplectic, we use these nonlinear flags to describe a class of coadjoint orbits of the group of Hamiltonian diffeomorphisms, orbits that consist of weighted isotropic nonlinear flags.