Mathematics – Algebraic Geometry
Scientific paper
1994-05-30
Mathematics
Algebraic Geometry
21 pages, AMS-LaTeX
Scientific paper
A Theorem due to Guillemin and Sternberg about geometric quantization of Hamiltonian actions of compact Lie groups $G$ on compact Kaehler manifolds says that the dimension of the $G$-invariant subspace is equal to the Riemann-Roch number of the symplectically reduced space. Combined with the shifting-trick, this gives explicit formulas for the multiplicities of the various irreducible components. One of the assumptions of the Theorem is that the reduction is regular, so that the reduced space is a smooth symplectic manifold. In this paper, we prove a generalization of this result to the case where the reduced space may have orbifold singularities. Our proof uses localization techniques from equivariant cohomology, and relies in particular on recent work of Jeffrey-Kirwan and Guillemin. Since there are no complex geometry arguments involved, the result also extends to non Kaehlerian settings.
No associations
LandOfFree
On Riemann-Roch Formulas for Multiplicities 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 On Riemann-Roch Formulas for Multiplicities, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On Riemann-Roch Formulas for Multiplicities will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-582622