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 (2)

• Quasi-particles models for the representations of Lie algebras and geometry of flag manifold
• Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, II: higher level case

Cited by in corpus (15)

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• Combinatorial bases of Feigin-Stoyanovsky's type subspaces of level 1 standard modules for $\tilde{\mathfrak sl}(\ell+1,\C)$
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• Characters of Feigin-Stoyanovsky's type subspaces of level one modules for affine Lie algebras of types $A_{\ell }^{(1)}$ and $D_4^{(1)}$
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• Combinatorial bases of principal subspaces of modules for twisted affine Lie algebras of type $A_{2l-1}^{(2)}$, $D_l^{(2)}$, $E_6^{(2)}$ and $D_4^{(3)}$
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• Quasi-particle bases of principal subspaces of the affine Lie algebra of type $G_2^{(1)}$
• Recurrence relations for characters of affine Lie algebra $A_{\ell }^{(1)}$
• Presentations of Feigin-Stoyanovsky's type subspaces of standard modules for affine Lie algebras of type $C_{\ell }^{(1)}$
• Particle basis of Feigin-Stoyanovsky's type subspaces of level $1$ ${\widetilde{\mathfrak{sl}}}_{\ell +1}(\mathbb{C})$-modules