Intertwining vertex operators and certain representations of sl(n)^

Abstract

We study the principal subspaces, introduced by B. Feigin and A. Stoyanovsky, of the level 1 standard modules for $\hat{\goth{sl}(l+1)}$ with $l\ge 2$. 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 S. Capparelli, J. Lepowsky and A. 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 G. Georgiev using a different method.

38 pages; v2: an error corrected, other minor changes

References in corpus (1)

• Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, II: higher level case

Cited by in corpus (6)

• Combinatorial bases of Feigin-Stoyanovsky's type subspaces of higher-level standard $\tilde{\gsl}(\ell+1,\C)$-modules
• Vertex-algebraic structure of the principal subspaces of level one modules for the untwisted affine Lie algebras of types A,D,E
• Combinatorial bases of Feigin-Stoyanovsky's type subspaces of level 2 standard modules for $D_4^{(1)}$
• Combinatorial bases of Feigin-Stoyanovsky's type subspaces of level 1 standard modules for $\tilde{\mathfrak sl}(\ell+1,\C)$
• Principal subspaces of higher-level standard sl(3)^-modules
• Recurrence relations for characters of affine Lie algebra $A_{\ell }^{(1)}$