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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 

 

Nilpotent orbits, normality and Hamiltonian group actions


Authors: Ranee Brylinski and Bertram Kostant
Journal: Bull. Amer. Math. Soc. 26 (1992), 269-275
MSC (2000): Primary 22E46; Secondary 58F06
MathSciNet review: 1119160
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Abstract: Let M be a G-covering of a nilpotent orbit in $ \mathfrak{g}$ where G is a complex semisimple Lie group and $ \mathfrak{g} = {\text{Lie}}(G)$. We prove that under Poisson bracket the space $ R[2]$ of homogeneous functions on M of degree 2 is the unique maximal semisimple Lie subalgebra of $ R = R(M)$ containing $ \mathfrak{g}$. The action of $ \mathfrak{g}'\simeq R[2]$ exponentiates to an action of the corresponding Lie group $ G'$ on a $ G'$-cover $ M'$ of a nilpotent orbit in $ \mathfrak{g}'$ such that M is open dense in $ M'$. We determine all such pairs $ (\mathfrak{g}\,\, \subset \,\,\mathfrak{g}')$.


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DOI: https://doi.org/10.1090/S0273-0979-1992-00271-9
Article copyright: © Copyright 1992 American Mathematical Society