VERTEX-ALGEBRAIC STRUCTURE OF THE PRINCIPAL SUBSPACES OF CERTAIN $A_{1}^{(1)}$-MODULES, I: LEVEL ONE CASE

Abstract

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 [Formula: see text]-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.