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

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.

v2. 28 pages, 18 figures, more details are added, errors are corrected

References in corpus (2)

• On the f-vectors of Gelfand-Cetlin polytopes
• Lagrangian fibers of Gelfand-Cetlin systems