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

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

2006-11-17

arxiv.org/abs/math/0611534v2

Comm. in Contemp. Math. 10 (2008), 47-79

Mathematics

Quantum Algebra

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

Scientific paper

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 $l \geq 2$. 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.

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