PIRSA:17010061 Scientific Series Mathematical physics

DOI10.48660/17010061

Series: Mathematical Physics

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}}
}

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.

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