Kac-Moody algebras in Deligne's Category

TL;DR

This paper extends the concept of Kac-Moody Lie algebras to Deligne Categories and establishes the Kac-Weyl formula for their integrable representations, broadening the scope of algebraic structures in category theory.

Contribution

It introduces a generalized framework for Kac-Moody algebras within Deligne Categories and derives the Kac-Weyl formula in this new setting.

Findings

Generalization of Kac-Moody algebras to Deligne Categories

Derivation of the Kac-Weyl formula for these generalized algebras

Extension of previous results by A. Pakharev

Abstract

We generalize the notion of a Kac-Moody Lie algebra to the setting of Deligne Categories. Then we derive the Kac-Weyl formula for the category $\mathcal{O}$ integrable representations for such an algebra. This paper generalizes results of A. Pakharev \cite{AP}.