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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

$K$-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
Email: chuah@math.nctu.edu.tw

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03434-X
PII: S 0002-9939(96)03434-X
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