The representation theory of vertex operator algebras is in fact equivalent to two-dimensional chiral conformal field theory. This is an introductory course on the representation theory of vertex operator algebras. In this course I will cover the following topics:
- Vertex operator algebras, modules and intertwining operators. (I will go through this part quickly if the students know some basic material on vertex operator algebras, for example, from Lepowsky's course in Fall 2021.)
- Definitions of conformal field theory, modular functor and weakly conformal field theory.
- Convergence, associativity and commutativity of intertwining operators.
- Tensor products of modules for a vertex operator algebra.
- Introduction to the tensor category of modules for a vertex operator algebra.
- Associative algebras and intertwining operators.
Text: Lecture notes:
- For topic 1 above: Yi-Zhi Huang, Lecture notes on vertex algebras and quantum vertex algebras:
pdf file
- Lecture notes for topics 2 to 6: Yi-Zhi Huang, Lecture notes on the representation theory of vertex operator algebras
and conformal field theory:
pdf file
References
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