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arXiv · 1806.01529

Lagrangian fibers of Gelfand--Cetlin systems of $\mathrm{SO}(n)$-type

Yunhyung Cho·Yoosik Kim
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Abstract

In this paper, we study the Gelfand--Cetlin systems and polytopes of the co-adjoint $\mathrm{SO}(n)$-orbits. We describe the face structure of Gelfand--Cetlin polytopes and iterated bundle structure of Gelfand--Cetlin fibers in terms of combinatorics on the ladder diagrams. Using this description, we classify all Lagrangian fibers.

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Yunhyung Cho, Yoosik Kim. 2018-06-05. Lagrangian fibers of Gelfand--Cetlin systems of $\mathrm{SO}(n)$-type. https://arxiv.org/abs/1806.01529

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