Localization of highest weight modules of a class of extended affine Lie algebras

In 2006, Gao and Zeng (Gao and Zeng, 2006) gave the free field realizations of highest weight modules over the extended affine Lie algebras gl2(Cq)̂ for any nonzero q∈C. In the present paper, applying the technique of localization to those free field realizations, we construct a class of new weight modules with infinite dimensional weight multiplicities over gl2(Cq)̂. We give necessary and sufficient conditions for these modules to be irreducible. In this way, we construct free field realizations for a class of simple weight modules with infinite dimensional weight multiplicities over gl2(Cq)̂ for any nonzero q∈C.