PIRSA:16010071

Cluster Structures on Higher Teichmuller Spaces for Classical Groups - Ian Le

(2016). Cluster Structures on Higher Teichmuller Spaces for Classical Groups - Ian Le. Perimeter Institute. https://pirsa.org/16010071

Cluster Structures on Higher Teichmuller Spaces for Classical Groups - Ian Le. Perimeter Institute, Jan. 07, 2016, https://pirsa.org/16010071 

          @misc{ pirsa_PIRSA:16010071,
            doi = {10.48660/16010071},
            url = {https://pirsa.org/16010071},
            author = {},
            keywords = {Mathematical physics},
            language = {en},
            title = {Cluster Structures on Higher Teichmuller Spaces for Classical Groups - Ian Le},
            publisher = {Perimeter Institute},
            year = {2016},
            month = {jan},
            note = {PIRSA:16010071 see, \url{https://pirsa.org}}
          }
Talk number
PIRSA:16010071
Collection
Talk Type
Subject
Abstract

Let $S$ be a surface, $G$ a semi-simple group of type B, C or D. I will explain why the moduli space of framed local systems $A_{G,S}$ defined by Fock and Goncharov has the structure of a cluster variety, and fits inside a larger structure called a cluster ensemble. This was previously known only in type A. This gives a more direct proof of results of Fock and Goncharov for the symplectic and spin groups, and also allows one to quantize higher Teichmuller space in these cases. If time permits, I hope to talk about applications to counting tensor invariants of finite dimensional representations of these groups.