Annihilators of Simple Integrable Weight sl(∞)-Modules

Let g = sl() .We compute the annihilators of a class of simple integrable weight gmodules with finite-dimensional weight spaces.It is a claim of I. Dimitrov, that this class exhausts all simple integrable weight g-modules with finite-dimensional weight spaces.The main feature of interest is that Dimitrov's modules contains non highest weight modules.Here we provide another construction for these modules, which allows to apply recent results of A. Petukhov and I. Penkov to compute such annihilators.