#### Hall 123

#### Yangians and R-matrices

#### Sachin Gautam

##### Perimeter Institute

*The Yang-Baxter equation and its study originated in 1970's. This equation is a sufficient condition for solvability of six vertex models of statistical mechanics, and its solutions are called R-matrices. A decade of research went into defining quantum groups as a uniform way to construct these R-matrices.*

We will focus on one of these quantum groups, namely Yangians. These are certain Hopf algebras introduced by Drinfeld in 1983, which come equipped with a universal R-matrix: a formal series in 1/u with coefficients from the tensor square of Yangian. This series (formally) satisfies the Yang-Baxter equation.

In this talk I will discuss the analytic properties of Drinfeld's universal R-matrix once evaluated on a pair of finite-dimensional representations of the Yangian. Spoiler alert: this series does not converge in any neighborhood of infinity and its coefficients can be expressed in terms of Bernoulli numbers.

The results presented in this talk were obtained jointly with V. Toledano Laredo.

Done