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 give explicit symplectic isomorphisms from twisted cotangent bundles of the complex generalized flag varieties, whose transition functions are given by affine transformations instead of linear transformations, onto the complex coadjoint semisimple orbits. Moreover, the isomorphisms are shown to be $G$-equivariant.

11pages (ver.1); 15pages, major modification, corrected errors (ver.2); 16pages, specified p=q=1 (i.e., G=SL_2 case) in ex.3.11 instead of arbitrary p, q (ver.3); 17pages, added a corollary and a proposition as an application of the main theorem (ver4)