PIRSA:18010079

Monodromy representations of elliptic braid groups

Yang, Y. (2018). Monodromy representations of elliptic braid groups. Perimeter Institute. https://pirsa.org/18010079

Yang, Yaping. Monodromy representations of elliptic braid groups. Perimeter Institute, Jan. 15, 2018, https://pirsa.org/18010079 

          @misc{ pirsa_PIRSA:18010079,
            doi = {10.48660/18010079},
            url = {https://pirsa.org/18010079},
            author = {Yang, Yaping},
            keywords = {Mathematical physics},
            language = {en},
            title = {Monodromy representations of elliptic braid groups},
            publisher = {Perimeter Institute},
            year = {2018},
            month = {jan},
            note = {PIRSA:18010079 see, \url{https://pirsa.org}}
          }

Yaping Yang University of Melbourne

DOI 10.48660/18010079
Collection
Talk Type Scientific Series
Subject

Abstract

In my talk, I will briefly review the representation theoretical construction of conformal blocks attached to an affine Kac-Moody algebra and a smooth algebraic curve with marked points. I will focus on the case when the algebraic curve is an elliptic curve. The bundle of conformal blocks carries a canonical flat connection: the Knizhnik-Zamolodchikov-Bernard (KZB) equation. There are various generalizations of the KZB equation. I will talk about one generalization that constructed by myself and Toledano Laredo recently: the elliptic Casimir connection. It is a holonomic system of differential equations with regular singularities on elliptic curve with marked points, taking values in a deformation of the double current algebra g[u, v] defined by Guay. The monodromy of elliptic Casimir connection leads to interesting representations of the elliptic braid groups.