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

Author: 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.

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Additional Information

Meng-Kiat Chuah
Affiliation: Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan

Received by editor(s): December 5, 1994
Received by editor(s) in revised form: April 24, 1995
Communicated by: Roe Goodman
Article copyright: © Copyright 1996 American Mathematical Society