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

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

2009-08-27

arxiv.org/abs/0908.4054v2

Mathematics

Quantum Algebra

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

Scientific paper

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.

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