New families of irreducible weight modules over [formula omitted

Abstract

Let n>1 be an integer, α∈Cn, b∈C, and V a gln-module. We define a class of weight modules Fbα(V) over sln+1 using the restriction of modules of tensor fields over the Lie algebra of vector fields on n-dimensional torus. In this paper we consider the case n=2 and prove the irreducibility of such 5-parameter sl3-modules Fbα(V) generically. All such modules have infinite dimensional weight spaces and lie outside of the category of Gelfand–Tsetlin modules. Hence, this construction yields new families of irreducible sl3-modules.