CLUSTER STRUCTURES on HIGHER TEICHMULLER SPACES for CLASSICAL GROUPS

Ian Tuan-Yen Le

doi:10.1017/fms.2019.5

CLUSTER STRUCTURES on HIGHER TEICHMULLER SPACES for CLASSICAL GROUPS

Ian Tuan-Yen Le^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

5 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 language	English (US)
Journal	Forum of Mathematics, Sigma
DOIs	https://doi.org/10.1017/fms.2019.5
State	Accepted/In press - 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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10.1017/fms.2019.5

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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 {\'E}tudes 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.",

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N2 - 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.

AB - 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.

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KW - 2010 Mathematics Subject Classification:

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JF - Forum of Mathematics, Sigma

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CLUSTER STRUCTURES on HIGHER TEICHMULLER SPACES for CLASSICAL GROUPS

Abstract

Keywords

ASJC Scopus subject areas

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