Adjoint orbits of semi-simple Lie groups and Lagrangean submanifolds

TL;DR

This paper explores the symplectic geometry of adjoint orbits in semi-simple Lie groups, providing multiple realizations and identifying Lagrangian submanifolds within these orbits.

Contribution

It introduces new realizations of adjoint orbits and characterizes Lagrangian submanifolds, enhancing understanding of their geometric structure.

Findings

Multiple realizations of adjoint orbits are provided.

Identification of a family of Lagrangian submanifolds within the orbits.

Insights into the symplectic geometry of semi-simple Lie group orbits.

Abstract

We give various realizations of the adjoint orbits of a semi-simple Lie group and describe their symplectic geometry. We then use these realizations to identify a family of Lagrangean submanifolds of the orbits.