The categories of representations and holomorphic maps into Grassmannians

Key Points

• The study aims to identify the relationships between unitary representations of semisimple Lie groups and holomorphic maps into Grassmannians.
• Analyzed the category of unitary representations of semisimple Lie groups
• Explored the properties of holomorphic maps into Grassmannians
• Examined gauge conditions of Hermitian vector bundles
• Established isomorphism between unitary representations and holomorphic maps
• Demonstrated implications for the structure of flag manifolds
• Highlighted significance of gauge conditions for vector bundles