INTERTWINING VERTEX OPERATORS AND CERTAIN REPRESENTATIONS OF $\widehat{\mathfrak{sl}(n)}$

Abstract

We study the principal subspaces, introduced by Feigin and Stoyanovsky, of the level 1 standard modules for [Formula: see text] with l ≥ 2. In this paper, we construct exact sequences which give us a complete set of recursions that characterize the graded dimensions of the principal subspaces of these representations. This problem can be viewed as a continuation of a new program to obtain Rogers–Ramanujan-type recursions, which was initiated by Capparelli, Lepowsky and Milas. In order to prove the exactness of the sequences, we use intertwining vertex operators and we supply a proof of the completeness of a list of relations for the principal subspaces. By solving these recursions we recover the graded dimensions of the principal subspaces, previously obtained by Georgiev using a different method.