Symplectic coordinates on PSL3(R)-Hitchin components
- Authors
- Choi, Suhyoung; Jung, Hongtaek; Kim, Hong Chan
- Issue Date
- 2020
- Publisher
- INT PRESS BOSTON, INC
- Keywords
- Hitchin component; Goldman coordinates; Darboux coordinates
- Citation
- PURE AND APPLIED MATHEMATICS QUARTERLY, v.16, no.5, pp.1321 - 1386
- Indexed
- SCIE
SCOPUS
- Journal Title
- PURE AND APPLIED MATHEMATICS QUARTERLY
- Volume
- 16
- Number
- 5
- Start Page
- 1321
- End Page
- 1386
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/59032
- ISSN
- 1558-8599
- Abstract
- Goldman parametrizes the PSL3(R)-Hitchin component of a closed oriented hyperbolic surface of genus g by 16(g) - 16 parameters. Among them, 10(g) - 10 coordinates are canonical. We prove that the PSL3(R)-Hitchin component equipped with the Atiyah-Bott-Goldman symplectic form admits a global Darboux coordinate system such that the half of its coordinates are canonical Goldman coordinates. To this end, we show a version of the action-angle principle and the Zocca-type decomposition formula for the symplectic form of H. Kim and Guruprasad-Huebschmann-Jeffrey-Weinstein given to symplectic leaves of the Hitchin component.
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