Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

$K$ -invariant Kaehler structures on $K_{% \mathbf {C}}/N$ and the associated line bundles

Author(s): Meng-Kiat Chuah
Journal: Proc. Amer. Math. Soc. 124 (1996), 3481-3491.
MSC (1991): Primary 53C55
MathSciNet review: 1340378
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Abstract: Let $K$ be a compact semi-simple Lie group, and let $N$ be a maximal unipotent subgroup of the complexified group $K_{% \mathbf {C}}$ . In this paper, we classify all the $K$ -invariant Kaehler structures on $K_{% \mathbf {C}}/N$ . For each Kaehler structure $\omega$ , let ${% \mathbf {L}}$ be the line bundle with connection whose curvature is $\omega$ . We then study the holomorphic sections of ${% \mathbf {L}}$ , which constitute a $K$ -representation space.

References:

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