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The Centralizer of Invariant Functions and Division Properties of the Moment Map

Eugene Lerman·Yael Karshon
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Abstract

Let Phi : M --> g^* be a proper moment map associated to an action of a compact connected Lie group, G, on a connected symplectic manifold, (M,ω). A collective function is a pullback via Φof a smooth function on g^*. In this paper we present four new results about the relationship between the collective functions and the G-invariant functions in the Poisson algebra of smooth functions on M.

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Eugene Lerman, Yael Karshon. 1996-09-25. The Centralizer of Invariant Functions and Division Properties of the Moment Map. https://arxiv.org/abs/dg-ga/9506008

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