Nilpotent orbits, normality and Hamiltonian group actions
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- by Ranee Brylinski and Bertram Kostant PDF
- Bull. Amer. Math. Soc. 26 (1992), 269-275 Request permission
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 $(\mathfrak {g} \subset \mathfrak {g}’)$.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Bull. Amer. Math. Soc. 26 (1992), 269-275
- MSC (2000): Primary 22E46; Secondary 58F06
- DOI: https://doi.org/10.1090/S0273-0979-1992-00271-9
- MathSciNet review: 1119160