Kaehler structures on Kc/(P,P)
dg-ga
2008-02-03 v2 Differential Geometry
Abstract
Let K be a compact semi-simple Lie group. We classify K-invariant Kaehler structures on the space Kc/(P,P), where Kc is the complexification of K, P is a parabolic subgroup of Kc, and (P,P) the commutator subgroup. For each Kaehler structure, we study its moment map and associated pre-quantum line bundle for geometric quantization. Some holomorphic sections of the line bundle form a unitary K-representation space, and we study the multiplicity of its irreducible subrepresentations.
Cite
@article{arxiv.dg-ga/9608008,
title = {Kaehler structures on Kc/(P,P)},
author = {Meng-Kiat Chuah},
journal= {arXiv preprint arXiv:dg-ga/9608008},
year = {2008}
}
Comments
LaTex 2.09, 30 pages. To appear in Trans. AMS. [email protected]