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.
- Publication:
-
arXiv e-prints
- Pub Date:
- February 2011
- DOI:
- 10.48550/arXiv.1102.1494
- arXiv:
- arXiv:1102.1494
- Bibcode:
- 2011arXiv1102.1494H
- Keywords:
-
- Mathematics - Differential Geometry;
- 53D20;
- 22F30
- E-Print:
- 11pages (ver.1)