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

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.

References in corpus (2)

• Categories O for Dynkin Borel Subalgebras of Root-Reductive Lie Algebras
• Simple bounded weight modules of $\mathfrak{sl}(\infty )$, $\mathfrak{o}(\infty )$, $\mathfrak{sp}(\infty )$