Affine Lie algebras and tensor categories
Abstract
We review briefly the existing vertex-operator-algebraic constructions of various tensor category structures on module categories for affine Lie algebras. We discuss the results first conjectured in the work of Moore and Seiberg that led us to the construction of the modular tensor category structure in the positive integral level case. Then we review the existing constructions and results in the following three cases: (i) the level plus the dual Coxeter number is not a nonnegative rational number, (ii) the level is a positive integer and (iii) the level is an admissible number. We also present several open problems.
Cite
@article{arxiv.1811.05123,
title = {Affine Lie algebras and tensor categories},
author = {Yi-Zhi Huang},
journal= {arXiv preprint arXiv:1811.05123},
year = {2018}
}
Comments
14 pages. For the proceedings of the "10th Seminar on Conformal Field Theory: A conference on Vertex Algebras and Related Topics" held at Research Institute for Mathematical Sciences, Kyoto University, Kyoto, April 23 - 27, 2018