Symplectic coordinates on PSL3(R)-Hitchin components

被引：0

作者：

Choi, Suhyoung ^{[1
]}

Jung, Hongtaek ^{[2
]}

Kim, Hong Chan ^{[3
]}

机构：

[1] Korea Adv Inst Sci & Technol, Dept Math Sci, Daejeon, South Korea

[2] Inst for Basic Sci Korea, Ctr Geometry & Phys, Pohang, South Korea

[3] Korea Univ, Dept Math Educ, Seoul, South Korea

来源：

PURE AND APPLIED MATHEMATICS QUARTERLY | 2020年 / 16卷 / 05期

关键词：

Hitchin component; Goldman coordinates; Darboux coordinates; REAL PROJECTIVE-STRUCTURES; MODULI SPACES; GROUP SYSTEMS; LIE-GROUPS; REPRESENTATIONS; LECTURES; FLOWS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1321 / 1386

页数：66