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Tohoku Mathematical Journal
SECOND SERIES VOL. 66, NO. 4
|Tohoku Math. J.|
66 (2014), 563-581
A TWISTED MOMENT MAP AND ITS EQUIVARIANCE
(Received November 9, 2012, revised November 21, 2013)
Let $G$ be a linear connected complex reductive Lie group. The purpose of this paper is to construct a $G$-equivariant symplectomorphism in terms of local coordinates from a holomorphic twisted cotangent bundle of the generalized flag variety of $G$ onto the semisimple coadjoint orbit of $G$. As an application, one can obtain an explicit embedding of a noncompact real coadjoint orbit into the twisted cotangent bundle.
Mathematics Subject Classification.
Primary 53D20; Secondary 22F30.
Key words and phrases.
Twisted moment map, $G$-equivariance, holomorphic twisted cotangent bundle, complex coadjoint orbit, symplectic isomorphism.
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