Seminar
On the multiplet Walgebras

Hold Date 
20220520 16:00～20220520 17:00 


Place 
Room C513 and Zoom meeting 


Object person 



Speaker 
Shoma Sugimoto (Kyushu University) 

Vertex operator algebra (VOA) was introduced in the 1980s as a mathematical formulation of twodimensional conformal field theories and is an interesting subject that relates to various areas of mathematics. Until now, semisimple VOAs have been mainly studied, but recently, from the viewpoint of higherdimensional quantum field theory and quantum topology, the study of nonsemisimple VOAs (logVOAs) has attracted much attention. One of the main (and almost the only) known examples of logVOA is the multiple Walgebra (associated to a simple Lie algebra g) which has been well studied when g is of type A_1. However, the multiple Walgebra associated to a general g has a complicated structure and conventional algebraic methods do not work, so there have been no results for many years. In this talk, the speaker will prove various basic properties of multiple Walgebras using a geometric approach. First, we give the algebraic and geometric definitions of multiple Walgebras and show that they coincide (FeiginTipunin conjecture, 2010). This allows us to use various powerful theorems in geometry for the study of multiple Walgebras. In particular, by using a duality theorem, we construct irreducible modules, determine the G×W_k(g)module structures, and compute the qcharacters. Finally, we discuss the relationship between the aforementioned results and quantum topology, as well as future prospects.