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

Chuah, Meng-Kiat

doi:10.1090/S0002-9939-96-03434-X

$K$-invariant Kaehler structures on $K_{\mathbf {C}}/N$ and the associated line bundles
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Proc. Amer. Math. Soc. 124 (1996), 3481-3491 Request permission

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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