Abstract:

One of the most fundamental problems in the study of a 2-dimensional (super)conformal field theory is to compute fusion rules between modules over the corresponding vertex operator superalgebra (VOSA). In order to compute fusion rules, I. Frenkel and Y. Zhu developed the theory of Frenkel--Zhu bimodules. In the theory the (twisted) Zhu's algebra associated with the VOSA, which is originally introduced by Y. Zhu, plays a prominent role. In this talk I will first give a brief review on the representation theory of the N=2 superconformal algebra and the corresponding VOSA. Then I will explain recent results on the twisted Zhu's algebra of the N=2 VOSA, which are based on joint work with S. Koshida (the Univ. of Tokyo).