Kaehler structures on Kc/(P,P)

Details Kaehler structures on Kc/(P,P) Kaehler structures on Kc/(P,P)

1996-08-28

arxiv.org/abs/dg-ga/9608008v2

Mathematics

Differential Geometry

LaTex 2.09, 30 pages. To appear in Trans. AMS. chuah@math.nctu.edu.tw

Scientific paper

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.

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