On the dimensions of vector spaces concerning holomorphic vector bundles over elliptic orbits

Nobutaka Boumuki

doi:10.21099/tkbjm/20224602217

Abstract

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.

Citation

Download Citation

Nobutaka Boumuki. "On the dimensions of vector spaces concerning holomorphic vector bundles over elliptic orbits." Tsukuba J. Math. 46 (2) 217 - 253, December 2022. https://doi.org/10.21099/tkbjm/20224602217

Information

Published: December 2022

First available in Project Euclid: 17 March 2023

MathSciNet: MR4561579

zbMATH: 1517.32052

Digital Object Identifier: 10.21099/tkbjm/20224602217

Subjects:

Primary: 32M10

Secondary: 17B10 , 17B20 , 17B22

Keywords: elliptic (adjoint) orbit , highest weight , homogeneous holomorphic vector bundle , homogeneous pseudo-Kähler manifold , maximal compact subalgebra , semisimple Lie group

Abstract

Citation

Information

KEYWORDS/PHRASES

PUBLICATION TITLE:

PUBLICATION YEARS