Speaker : Mr. Ryo Sato (University of Tokyo) Title : On Equivalence between $\widehat{sl}_2$ and the $N=2$ superconformal algebra Time : 2017-02-24 (Fri) 11:00 - 12:00 Place : Seminar Room 714, Institute of Mathematics (NTU Campus) Abstract: The N=2 superconformal algebra (SCA) is an infinite-dimensional Lie superalgebra which is obtained as a supersymmetric generalization of the Virasoro algebra. The representation theory of the N=2 SCA involves several remarkable topics, for example, the (mock) modular property of characters and the braided tensor structure with respect to the fusion product. B. Feigin, A. Semikhatov and I. Tipunin discovered that general highest weight modules over the N=2 SCA correspond to certain non-standard highest weight modules over $\widehat{sl}_{2}$ via the Kazama-Suzuki coset construction. In this talk, we give (block-wise) equivalences between the categries of certain weight modules over $\widehat{sl}_{2}$ and the N=2 SCA by refining their work.