Representation Theory Seminar

ABSTRACT: Conformal superalgebras establish a rigorous algebraic foundation for the theory of vertex algebras and, more generally, conformal field theory. In particular, they are closely related (and generalize) the superconformal algebras known to physicists. More generally, conformal algebras provide a powerful formalism for the study of infinite-dimensonal Lie algebras and their representations. I will discuss the recently obtained classification of finite conformal superalgebras and explain what makes some of them suitable for physical theories. Then I will describe the general set-up for "conformal representation theory" and related combinatorial and algebraic problems.