PIRSA:17010061

Positive representations of quantum groups and higher Teichmuller theory

Shapiro, A. (2017). Positive representations of quantum groups and higher Teichmuller theory. Perimeter Institute. https://pirsa.org/17010061

Shapiro, Alexander. Positive representations of quantum groups and higher Teichmuller theory. Perimeter Institute, Jan. 23, 2017, https://pirsa.org/17010061 

          @misc{ pirsa_PIRSA:17010061,
            doi = {10.48660/17010061},
            url = {https://pirsa.org/17010061},
            author = {Shapiro, Alexander},
            keywords = {Mathematical physics},
            language = {en},
            title = {Positive representations of quantum groups and higher Teichmuller theory},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {jan},
            note = {PIRSA:17010061 see, \url{https://pirsa.org}}
          }

Alexander Shapiro

University of Edinburgh

Talk number
PIRSA:17010061
Collection
Talk Type
Subject
Abstract

Positive representations are infinite-dimensional bimodules for the quantum group and its modular dual U_{q^\vee}(\mathfrak{g}^\vee)where both act by positive essentially self-adjoint operators. Fifteen years ago Ponsot and Teschner showed that positive representations are closed under taking tensor products in the case g = sl(2), however similar conjecture remains open for all other types. I will outline its proof for g = sl(n) based on a joint work in progress with Gus Schrader. I will also argue that this conjecture is the key step towards the proof of the modular functor conjecture for quantized higher Teichmuller theories.