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

Abstract

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 [С1].