What question did this study set out to answer?

The study aims to identify the relationships between unitary representations of semisimple Lie groups and holomorphic maps into Grassmannians.

April 17, 2026Open Access

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

Abstract

We will show that the category of the unitary representations of a compact, connected, simply connected, semisimple Lie group is isomorphic to one of full holomorphic maps of a flag manifold to complex Grassmannians with gauge condition for semipositive Hermitian holomorphic homogeneous vector bundles.

The categories of representations and holomorphic maps into Grassmannians

Key Points

Abstract

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