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

Published 5 Jun 2018 in math.SG | (1806.01529v2)

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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