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Advanced Algebra and GeometryGeometry and complex manifoldsHomotopy and Cohomology in Algebraic Topology

The categories of representations and holomorphic maps into Grassmannians

Yasuyuki Nagatomo

2026.4.15Proceedings of the American Mathematical Society, Series B

DOI: 10.1090/bproc/276

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.

Citation format

NAGATOMO, Yasuyuki. The categories of representations and holomorphic maps into grassmannians. Proceedings of the American Mathematical Society, Series B, 2026, 13(5): 37–43.