Symplectic slice for subgroup actions

Abstract

Given a symplectic manifold $(M,\omega )$ endowed with a proper Hamiltonian action of a Lie group $G$, we consider the action induced by a Lie subgroup $H$ of $G$. We propose a construction for two compatible Witt-Artin decompositions of the tangent space of $M$, one relative to the $G$-action and one relative to the $H$-action. In particular, we provide an explicit relation between the respective symplectic slices.

18 pages

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