Tsukuba J. Math. 46 (2), 217-253, (December 2022) DOI: 10.21099/tkbjm/20224602217
KEYWORDS: homogeneous pseudo-Kähler manifold, elliptic (adjoint) orbit, semisimple Lie group, maximal compact subalgebra, homogeneous holomorphic vector bundle, highest weight, 32M10, 17B20, 17B10, 17B22
In this paper, we study the complex vector space of holomorphic cross-sections of a homogeneous holomorphic vector bundle over an elliptic adjoint orbit, and give a sufficient condition for the vector space to be finite-dimensional.