PIRSA:16110027

Quantum groups from character varieties

Schrader, G. (2016). Quantum groups from character varieties. Perimeter Institute. https://pirsa.org/16110027

Schrader, Gus. Quantum groups from character varieties. Perimeter Institute, Nov. 10, 2016, https://pirsa.org/16110027 

          @misc{ pirsa_PIRSA:16110027,
            doi = {10.48660/16110027},
            url = {https://pirsa.org/16110027},
            author = {Schrader, Gus},
            keywords = {Mathematical physics},
            language = {en},
            title = {Quantum groups from character varieties},
            publisher = {Perimeter Institute},
            year = {2016},
            month = {nov},
            note = {PIRSA:16110027 see, \url{https://pirsa.org}}
          }

Gus Schrader

University of California, Berkeley

Talk number
PIRSA:16110027
Collection
Talk Type
Subject
Abstract

Quantum groups from character varieties
Abstract: The moduli spaces of local systems on marked surfaces enjoy many nice properties. In particular, it was shown by Fock and Goncharov that they form examples of cluster varieties, which means that they are Poisson varieties with a positive atlas of toric charts, and thus admit canonical quantizations. I will describe joint work with A. Shapiro in which we embed the quantized enveloping algebra U_q(sl_n) into the quantum character variety associated to a punctured disk with two marked points on its boundary. The construction is closely related to the (quantized) multiplicative Grothendieck-Springer resolution for SL_n. I will also explain how the R-matrix of U_q(sl_n) arises naturally in this topological setup as a (half) Dehn twist. Time permitting, I will describe some potential applications to the study of positive representations of the split real quantum group U_q(sl_n,R)