PIRSA:24030101

Video URL

https://pirsa.org/24030101

Factorisation Quantum Groups

Latyntsev, A. (2024). Factorisation Quantum Groups. Perimeter Institute for Theoretical Physics. https://pirsa.org/24030101

Latyntsev, Alexei. Factorisation Quantum Groups. Perimeter Institute for Theoretical Physics, Mar. 07, 2024, https://pirsa.org/24030101 

          @misc{ scivideos_PIRSA:24030101,
            doi = {10.48660/24030101},
            url = {https://pirsa.org/24030101},
            author = {Latyntsev, Alexei},
            keywords = {Mathematical physics},
            language = {en},
            title = {Factorisation Quantum Groups},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2024},
            month = {mar},
            note = {PIRSA:24030101 see, \url{https://scivideos.org/index.php/pirsa/24030101}}
          }

Alexei Latyntsev University of Southern Denmark

Talk numberPIRSA:24030101
DOI10.48660/24030101
Source RepositoryPIRSA
Collection
Talk Type Scientific Series
Subject

Abstract

This talk explains the theory of "factorisation" or "vertex algebra" analogues of the theory of quantum groups, (2312.07274).

We will first recap the theory of quantum groups and their connections to wider mathematics, due to Drinfeld, Etingof, Kazhdan, Jimbo, Reshetikhin, Turaev, and many others. We will then explain how to give a natural definition of "factorisation" version of these objects, give the basic structure theory about their categories of representations, and derive an explicit model for them. This relates to previous work of Etingof-Kazhdan and Frenkel-Reshetikhin.

We will sketch some physics heuristics for the above theory; briefly, our structures should appear on the category of line operators in 4d theories due to Costello, Witten and Yamazaki, e.g. on the representations Rep U_q(g^) of affine quantum groups.

We will then give some examples. The last part discusses the conjectures that naturally suggest themselves, for instance by analogy to the connections referred to above.

Prerequisites on chiral and vertex algebras will be given at a talk earlier in the week. (1-2pm Tuesday, Bob Room)

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