Combinatorics of infinite rank module categories over finite dimensional ${\mathfrak{sl}}_3$-modules in Lie-algebraic context

Abstract

We determine the combinatorics of transitive module categories over the monoidal category of finite dimensional ${\mathfrak{sl}}_3$-modules which arise when acting by the latter monoidal category on arbitrary simple ${\mathfrak{sl}}_3$-modules. This gives us a family of eight graphs which can be viewed as ${\mathfrak{sl}}_3$-generalizations of the classical infinite Dynkin diagrams.