Classification of simple Gelfand–Tsetlin modules of 𝔰𝔩(3)

Abstract

We provide a classification and an explicit realization of all simple Gelfand–Tsetlin modules of the complex Lie algebra [Formula: see text]. The realization of these modules, including those with infinite-dimensional weight spaces, is given via regular and derivative Gelfand–Tsetlin tableaux. Also, we show that all simple Gelfand–Tsetlin [Formula: see text]-modules can be obtained as subquotients of localized Gelfand–Tsetlin [Formula: see text]-injective modules.