Super Yangians: Where We Are Today
Abstract
Given any finite-dimensional simple Lie algebra a over $\mathbb{C}$, the Yangian $\operatorname{Y}(\mathfrak{g})$ is a certain unital associative $\mathbb{C}$-algebra. In particular, Yangians form a family of so-called quantum groups. The main property these algebras is the foundational fact that their representations produce rational solutions to the quantum Yang-Baxter equation. The structure and representation theory of Yangians has become a study in and of itself and has expanded to the study of super Yangians based on Lie superalgebras; however, the theory of super Yangians is comparatively less developed than its non-super counterpart. In this talk, we will survey what recent advancements have been made in the study of super Yangians and view what else remains to do.
