Vertex tensor category structure on a category of Kazhdan--Lusztig

Abstract

We incorporate a category of certain modules for an affine Lie algebra, of a certain fixed non-positive-integral level, considered by Kazhdan and Lusztig, into the representation theory of vertex operator algebras, by using the logarithmic tensor product theory for generalized modules for a vertex operator algebra developed by Huang, Lepowsky and the author. We do this by proving that the conditions for applying this general logarithmic tensor product theory hold. As a consequence, we prove that this category has a natural vertex tensor category structure, and in particular we obtain a new, vertex-algebraic, construction of the natural associativity isomorphisms and proof of their properties.

arXiv comment20 pages

References in corpus (2)

• Logarithmic tensor product theory for generalized modules for a conformal vertex algebra, Part I
• Categories of modules over an affine Kac-Moody algebra and the Kazhdan-Lusztig tensor product

Cited by in corpus (5)

• Logarithmic tensor product theory for generalized modules for a conformal vertex algebra, Part I
• Braided tensor categories of admissible modules for affine Lie algebras
• Gluing vertex algebras
• Bosonic ghostbusting -- The bosonic ghost vertex algebra admits a logarithmic module category with rigid fusion
• Cofiniteness conditions, projective covers and the logarithmic tensor product theory