Vertex tensor category structure on a category of Kazhdan-Lusztig
Vertex tensor category structure on a category of Kazhdan-Lusztig
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Kazhdan-Lusztig 范畴上的顶点张量范畴结构
DOI：
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发表时间：
2007
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通讯作者：
Lin Zhang
中科院分区：
文献类型：
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作者：
Lin Zhang
我们将 Kazhdan 和 Lusztig 考虑的仿射李代数的某些模（固定层，非正整数）的范畴纳入顶点算子代数的表示论中。我们使用由 Huang、Lepowsky 和作者开发的顶点算子代数的广义模块的对数张量积理论来实现这一点；我们证明了应用这种一般对数张量积理论的条件成立。因此，我们证明该范畴具有自然的顶点张量范畴结构，特别是我们获得了自然结合性同构的新的顶点代数构造及其性质的证明。
We incorporate a category considered by Kazhdan and Lusz- tig of certain modules (of a fixed level , not a positive integer) for an affine Lie algebra, into the representation theory of vertex operator al- gebras. 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.