Mathematics – Differential Geometry
Scientific paper
2008-12-15
Muenster J. Math. 2 (2009), 265-298
Mathematics
Differential Geometry
34 pages; v2: many local improvements, including many reflecting suggestions of the referee, including some important ones
Scientific paper
The coadjoint orbits of compact Lie groups carry many K\"ahler structures, which include a Riemannian metric and a complex structure. We provide a fairly explicit formula for the Levi-Civita connection of the Riemannian metric, and we use the complex structure to give a fairly explicit construction of a canonical Dirac operator for the Riemannian metric, in a way that avoids use of the Spin^c groups. Substantial parts of our results apply to compact almost-Hermitian homogeneous spaces, and to other connections besides the Levi-Civita connection. For these other connections we give a criterion that is both necessary and sufficient for their Dirac operator to be formally self-adjoint. We hope to use the detailed results given here to clarify statements in the literature of high-eneregy physics concerning "Dirac operators" for matrix algebras that converge to coadjoint orbits. To facilitate this we employ here only global methods -- we never use local coordinate charts, and we use the cross-section modules of vector bundles.
No associations
LandOfFree
Dirac operators for coadjoint orbits of compact Lie groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Dirac operators for coadjoint orbits of compact Lie groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dirac operators for coadjoint orbits of compact Lie groups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-349792