Hostname: page-component-7479d7b7d-qlrfm Total loading time: 0 Render date: 2024-07-14T01:07:33.522Z Has data issue: false hasContentIssue false
  • English
  • Français

Adjoint Orbits of Semi-Simple Lie Groups and Lagrangian Submanifolds

Part of: Symplectic geometry, contact geometry Lie groups

Published online by Cambridge University Press:  15 June 2016

Elizabeth Gasparim ,
Lino Grama  and
Luiz A. B. San Martin
Elizabeth Gasparim
Affiliation:
Departamento de Matemáticas, Universidad Católica del Norte, Avenida Angamos 0610, Antofagasta, Chile (etgasparim@gmail.com)
Lino Grama
Affiliation:
IMECC–UNICAMP, Departamento de Matemática, Rua Sérgio Buarque de Holanda 651, Cidade Universitária ‘Zeferino Vaz’, 13083-859 Campinas, Brazil (smartin@ime.unicamp.br; linograma@gmail.com)
Luiz A. B. San Martin
Affiliation:
IMECC–UNICAMP, Departamento de Matemática, Rua Sérgio Buarque de Holanda 651, Cidade Universitária ‘Zeferino Vaz’, 13083-859 Campinas, Brazil (smartin@ime.unicamp.br; linograma@gmail.com)
Get access Rights & Permissions [Opens in a new window]

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 Lagrangian submanifolds of the orbits.

Keywords

adjoint orbitssymplectic fibrationsLagrangian submanifoldsflag manifolds

MSC classification

Secondary: 22E30: Analysis on real and complex Lie groups 53D12: Lagrangian submanifolds; Maslov index
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 2 , May 2017 , pp. 361 - 385
Copyright
Copyright © Edinburgh Mathematical Society 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)