PIRSA:16010071 Scientific Series Mathematical physics

DOI10.48660/16010071

Series: Mathematical Physics

(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}}
}

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.

Resources

Next talk

Related Talks