Tohoku Mathematical Journal
2014
December
SECOND SERIES VOL. 66, NO. 4

Tohoku Math. J.
66 (2014), 563-581

Title A TWISTED MOMENT MAP AND ITS EQUIVARIANCE

Author Takashi Hashimoto

(Received November 9, 2012, revised November 21, 2013)
Abstract. 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.

To the top of this page

Back to the Contents