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 g l 2 ( C q ) ̂ 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 g l 2 ( C q ) ̂ . 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 g l 2 ( C q ) ̂ for any nonzero q ∈ C . [ABSTRACT FROM AUTHOR]