Affine Lie algebras and tensor categories

Speaker:Yi-Zhi Huang
Time: Tue 16:30-17:30, 2019-6-18
Venue:Lecture hall, 3rd floor of Jin Chun Yuan West Building


I will review the existing constructions of various tensor category structures on module categories for affine Lie algebras. I will discuss the results that were first conjectured in the work of Moore and Seiberg and that led us to the construction of the modular tensor category structure in the positive integral level case. Then I will 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. I will also present several open problems. I will give historical remarks in the talk to correct many misunderstandings and confusions existed in the literature.


Yi-Zhi Huang, Professor of Mathematics at Rutgers University. Co-Editor-in-Chief, Communications in Contemporary Mathematics. Member of the Editorial Board, New York Journal of Mathematics. His main research interest is the mathematical theory of quantum field theory and its application in algebra, topology, geometry, condensed matter physics and string theory. Bachelor of Science in Mechanics (predecessor of the Department of Aeronautics and Astronautics), Department of Mathematics, Fudan University. Master of Science, Institute of Mathematics, Fudan University. Ph. D. in Mathematics, Rutgers University.