Deformations of adjoint orbits for semisimple Lie algebras and Lagrangian submanifolds |
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Affiliation: | Imecc - Unicamp, Departamento de Matemática. Rua Sérgio Buarque de Holanda, 651, Cidade Universitária Zeferino Vaz. 13083-859 Campinas - SP, Brazil |
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Abstract: | We give a coadjoint orbit's diffeomorphic deformation between the classical semisimple case and the semi-direct product given by a Cartan decomposition. The two structures admit the Hermitian symplectic form defined in a semisimple complex Lie algebra. We provide some applications such as the constructions of Lagrangian submanifolds. |
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Keywords: | Adjoint orbits Homogeneous space Hermitian symplectic form Lagrangian submanifolds |
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