Monodromy representations of elliptic braid groups
APA
Yang, Y. (2018). Monodromy representations of elliptic braid groups. Perimeter Institute. https://pirsa.org/18010079
MLA
Yang, Yaping. Monodromy representations of elliptic braid groups. Perimeter Institute, Jan. 15, 2018, https://pirsa.org/18010079
BibTex
@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}} }
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.