A new construction of irreducible quasi-finite highest weight modules for toroidal 2

In this paper, we present a new free field(-like) construction of irreducible modules for toroidal 𝔰𝔩 2 with finite dimensional weight spaces and trivial central action. To this end, we also determine the irreducibility of certain Verma modules for generalized Takiff algebras associated to 𝔰𝔩 2 .