Explicit realization of irreducible representations of classical compact lie groups in the spaces of sections of line bundles

• Date: 1998
• Main Authors: Golod, P. I., Skrypnik, T. V., Голод, П. І., Скрипник, Т. В.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1998
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4818
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We use the Borel-Weil scheme for the construction of irreducible representations of compact Lie groups in the spaces of holomorphic sections of line bundles over homogeneous manifolds. We find the explicit form of the space of sections and construct an invariant scalar product. We show that the spac...