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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)
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Abstract

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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