Vertex tensor category structure on a category of Kazhdan-Lusztig
نویسنده
چکیده
We incorporate a category considered by Kazhdan and Lusztig of certain modules (of a fixed level , not a positive integer) for an affine Lie algebra, into the representation theory of vertex operator algebras. We do this using the logarithmic tensor product theory for generalized modules for a vertex operator algebra developed by Huang, Lepowsky and the author; we prove 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.
منابع مشابه
On the quantum Kazhdan-Lusztig functor
One of the most exciting developments in representation theory in the recent years was the discovery of the Kazhdan-Lusztig functor [KL93a, KL93b, KL94a, KL94b], which is a tensor functor from the fusion category of representations of an affine Lie algebra to the category of representations of the corresponding quantum group, and is often an equivalence of categories. Informally speaking, this ...
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