Imaginary Verma modules for the extended Affine Lie algebra $sl_2(C_q)$

We 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".