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arXiv · 2507.12785

The intersection of two real flag manifolds in a complex flag manifold

Osamu Ikawa·Hiroshi Iriyeh·Takayuki Okuda·Takashi Sakai·Hiroyuki Tasaki
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Abstract

We give a necessary and sufficient condition for two real flag manifolds, which are not necessarily congruent, in a complex flag manifold to intersect transversally in terms of the symmetric triad. Then we show that the intersection of two real flag manifolds is antipodal. As an application, we prove that any real flag manifold in a complex flag manifold is a globally tight Lagrangian submanifold.

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Osamu Ikawa, Hiroshi Iriyeh, Takayuki Okuda, Takashi Sakai, Hiroyuki Tasaki. 2025-07-17. The intersection of two real flag manifolds in a complex flag manifold. https://arxiv.org/abs/2507.12785

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