 

Lin Zhang
Vertex tensor category structure on a category of KazhdanLusztig


Published: 
June 28, 2008

Keywords: 
Vertex operator algebra, generalized module, logarithmic tensor product theory, vertex tensor category, braided tensor category 
Subject: 
17B69; 17B67; 81T40; 18D10 


Abstract
We incorporate a category considered by Kazhdan and
Lusztig of certain modules (of a fixed level ℓ, 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, vertexalgebraic, construction of the natural
associativity isomorphisms and proof of their properties.


Acknowledgements
Partial support from NSF grant DMS0070800 is gratefully acknowledged.


Author information
Department of Mathematics, Rutgers University, Piscataway, NJ 08854
linzhang@math.rutgers.edu

