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

Calinescu, Corina; Lepowsky, James; Milas, Antun

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

Authors

Calinescu, Corina

Lepowsky, James

Milas, Antun

Description

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.
20 pages. To appear in International J. of Math