A twisted moment map and its equivariance

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.