CLUSTER STRUCTURES on HIGHER TEICHMULLER SPACES for CLASSICAL GROUPS

Ian Tuan-Yen Le*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Let be a surface, a simply connected classical group, and the associated adjoint form of the group. We show that the moduli spaces of framed local systems and, which were constructed by Fock and Goncharov ['Moduli spaces of local systems and higher Teichmuller theory', Publ. Math. Inst. Hautes Études Sci. 103 (2006), 1-212], have the structure of cluster varieties, and thus together form a cluster ensemble. This simplifies some of the proofs in that paper, and also allows one to quantize higher Teichmuller space, which was previously only possible when was of type.

Original languageEnglish (US)
JournalForum of Mathematics, Sigma
DOIs
StateAccepted/In press - Jan 1 2019

Keywords

  • 13F60 (primary)
  • 15A72 (secondary)
  • 2010 Mathematics Subject Classification:

ASJC Scopus subject areas

  • Analysis
  • Theoretical Computer Science
  • Algebra and Number Theory
  • Statistics and Probability
  • Mathematical Physics
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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