Free field realizations of certain modules for affine Lie algebra $\widehat{sl}(n,\mathbb C)$

For the affine Lie algebra $\widehat{sl}(n,\mathbb C)$ we study a realization in terms of infinite sums of partial differential operators of a family of representations introduced in [BBFK]. These representations generalize a construction of Imaginary Verma modules [F1]. The realization constructed in the paper extends the free field realization of Imaginary Verma modules constructed by B. Cox [C1].