Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, I: level one case

Details Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, I: level one case Vertex-algebraic structure of the principal subspaces of certain A_1^(1)-modules, I: level one case

2007-04-13

arxiv.org/abs/0704.1759v1

Int.J.Math.19:71-92,2008

Mathematics

Quantum Algebra

20 pages. To appear in International J. of Math

Scientific paper

10.1142/S0129167X08004571

This is the first in a series of papers in which we study vertex-algebraic structure of Feigin-Stoyanovsky's principal subspaces associated to standard modules for both untwisted and twisted affine Lie algebras. A key idea is to prove suitable presentations of principal subspaces, without using bases or even ``small'' spanning sets of these spaces. In this paper we prove presentations of the principal subspaces of the basic A_1^(1)-modules. These convenient presentations were previously used in work of Capparelli-Lepowsky-Milas for the purpose of obtaining the classical Rogers-Ramanujan recursion for the graded dimensions of the principal subspaces.

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