2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61329We consider one of the most natural extended affine Lie lagebras, the algebra $sl_2({\mathbb C}_q)$ and begin a theory of its representations. In particular, we study a class of imaginary Verma modules, obtain a criterion of irreducibility and describe their submodule structure in "general position".Representation Theory17B67, 17B65text