Annihilators of simple integrable weight $\mathfrak{sl}(\infty)$-modules

TL;DR

This paper computes the annihilators of a broad class of simple integrable weight modules over the infinite-dimensional Lie algebra sl(), including non-highest weight modules, using a new construction that leverages recent results.

Contribution

It provides a new construction for simple integrable weight modules over sl(), enabling the computation of their annihilators, and confirms Dimitrov's claim about the class's exhaustiveness.

Findings

Computed annihilators for the class of modules

Included non-highest weight modules in the analysis

Applied recent results to extend understanding of module structure

Abstract

Let $\mathfrak{g}=\mathfrak{sl}(\infty)$. We compute the annihilators of a class of simple integrable weight $\mathfrak{g}$-modules with finite-dimensional weight spaces. It is a claim of I. Dimitrov, that this class exhausts all simple integrable weight $\mathfrak{g}$-modules with finite-dimensional weight spaces. The main feature of interest is that Dimitrov's class of modules contains non highest weight modules. Here we provide another construction for these modules, which allows to apply results of [PP18] to compute such annihilators.