Vertex-algebraic structure of the principal subspaces of level one modules for the untwisted affine Lie algebras of types A,D,E

Abstract

Generalizing some of our earlier work, we prove natural presentations of the principal subspaces of the level one standard modules for the untwisted affine Lie algebras of types A, D and E, and also of certain related spaces. As a consequence, we obtain a canonical complete set of recursions (q-difference equations) for the (multi-)graded dimensions of these spaces, and we derive their graded dimensions. Our methods are based on intertwining operators in vertex operator algebra theory.

arXiv comment25 pages, to appear in Journal of Algebra. v2: no changes

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• Ghost series and a motivated proof of the Andrews-Bressoud identities
• Principal subspaces for the affine Lie algebras in types $D$, $E$ and $F$
• Vertex operators and principal subspaces of level one for $U_q({\widehat{\mathfrak{sl}}}_2)$