Speaker: Steven Sam (UC San Diego)

Title: Curried Lie Algebras

Abstract: A representation of $gl(V)$ is a map $V \otimes V^* \otimes M \to M$ satisfying some conditions, or via currying, it is a map $V \otimes M \to V \otimes M$ satisfying different conditions. The latter formulation can be used in more general symmetric tensor categories where duals may not exist, such as the category of sequences of symmetric group representations under the induction product. Several other families of Lie algebras have such "curried" descriptions and their categories of representations have nice compact descriptions as representations of diagram categories, such as the (walled) Brauer category, partition category, and variants. I will explain a few examples in detail and how we came to this definition. This is joint work with Andrew Snowden.