$K$-invariant Kaehler structures on $K_{\mathbf {C}}/N$ and the associated line bundles
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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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Additional Information
- Meng-Kiat Chuah
- Affiliation: Department of Applied Mathematics, National Chiao Tung University, Hsinchu, Taiwan
- Email: chuah@math.nctu.edu.tw
- Received by editor(s): December 5, 1994
- Received by editor(s) in revised form: April 24, 1995
- Communicated by: Roe Goodman
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 3481-3491
- MSC (1991): Primary 53C55
- DOI: https://doi.org/10.1090/S0002-9939-96-03434-X
- MathSciNet review: 1340378