PIRSA:21020046

# On hidden quantum group symmetries in CFT

### APA

Peltola, E. (2021). On hidden quantum group symmetries in CFT. Perimeter Institute. https://pirsa.org/21020046

### MLA

Peltola, Eveliina. On hidden quantum group symmetries in CFT. Perimeter Institute, Feb. 25, 2021, https://pirsa.org/21020046

### BibTex

          @misc{ pirsa_21020046,
doi = {10.48660/21020046},
url = {https://pirsa.org/21020046},
author = {Peltola, Eveliina},
keywords = {Mathematical physics},
language = {en},
title = {On hidden quantum group symmetries in CFT},
publisher = {Perimeter Institute},
year = {2021},
month = {feb},
note = {PIRSA:21020046 see, \url{https://pirsa.org}}
}


Eveliina Peltola University of Bonn

Talk Type
Subject

## Abstract

"I discuss applications of a hidden $U_q(\mathfrak{sl}_2)$-symmetry in CFT with central charge $c \leq 1$ (focusing on the generic, semisimple case, with $c$ irrational). This symmetry provides a systematic method for solving Belavin-Polyakov-Zamolodchikov PDE systems, and in particular for explicit calculation of the asymptotics and monodromy properties of the solutions. Using a quantum Schur-Weyl duality, one can understand solution spaces of such PDE systems in a detailed way. The solutions, in turn, are useful both for CFT questions and for rigorous understanding of the connections of 2D CFT with critical models of statistical physics."