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Equivariant symplectic geometry of cotangent bundles, II

Dmitri A. Timashev
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Abstract

We examine the structure of the cotangent bundle $T^{*}X$ of an algebraic variety $X$ acted on by a reductive group $G$ from the viewpoint of equivariant symplectic geometry. In particular, we construct an equivariant symplectic covering of $T^{*}X$ by the cotangent bundle of a certain variety of horospheres in $X$, and integrate the invariant collective motion on $T^{*}X$. These results are based on a "local structure theorem" describing the action of a certain parabolic in $G$ on an open subset of $X$, which is interesting by itself.

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Dmitri A. Timashev. 2005-07-06. Equivariant symplectic geometry of cotangent bundles, II. https://arxiv.org/abs/math/0502284

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