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LAGRANGIAN FIBERS OF GELFAND–CETLIN SYSTEMS OF SO(n)-TYPE

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Abstract

In this paper, we study the Gelfand–Cetlin systems and polytopes of the co-adjoint 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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Authors and Affiliations

  1. Department of Mathematics Education, Sungkyunkwan University, Seoul, Republic of Korea

    YUNHYUNG CHO

  2. Department of Mathematics, Brandeis University, Waltham, MA, USA

    YOOSIK KIM

  3. Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA, USA

    YOOSIK KIM

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  1. YUNHYUNG CHO
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  2. YOOSIK KIM
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Correspondence to YOOSIK KIM.

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Yunhyung Cho is supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP; Ministry of Science, ICT & Future Planning.) (NRF-2020R1C1C1A01010972).

This work was initiated when the second named author was affiliated to IBS-CGP and was supported by IBS-R003-D1.

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CHO, Y., KIM, Y. LAGRANGIAN FIBERS OF GELFAND–CETLIN SYSTEMS OF SO(n)-TYPE. Transformation Groups 25, 1063–1102 (2020). https://doi.org/10.1007/s00031-020-09566-4

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  • DOI: https://doi.org/10.1007/s00031-020-09566-4

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