On the Lagrangian Embedding of \({\rm U}(n)\) in the Grassmannian \({\rm Gr} (n -1, 2 n -1)\)

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发表日期：

2025年3月1日

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N. Tyurin

摘要

Abstract

In the present paper we combine our previous results in the studies of Lagrangian geometry of the Grassmannian \({\rm Gr} (k, n)\) with the example of Lagrangian embedding of the full flag variety in the direct product of projective spaces, found by D. Bykov. As the result, we construct a Langrangian immersion of the group \({\rm U}(n)\) , as a submanifold, into the complex Grassmanian \({\rm Gr} (n-1, 2 n-1)\) equipped with the symplectic form, by the Plücker embedding.

DOI 10.1134/S1061920824601770