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

IF 1.7 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-05-05 DOI:10.1134/S1061920824601770

N. Tyurin

引用次数: 0

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

查看原文本刊更多论文

关于\({\rm U}(n)\)在格拉斯曼方程中的拉格朗日嵌入 \({\rm Gr} (n -1, 2 n -1)\)

在本文中，我们将前人关于格拉斯曼方程\({\rm Gr} (k, n)\)的拉格朗日几何的研究结果与D. Bykov在射影空间的直积中发现的全旗变化的拉格朗日嵌入的例子结合起来。因此，我们将群\({\rm U}(n)\)作为子流形，通过plicker嵌入构造为具有辛形式的复数Grassmanian \({\rm Gr} (n-1, 2 n-1)\)的朗朗日浸没。Doi 10.1134/ s1061920824601770

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.