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Representation theory of vertex operator algebras is equivalent to
two-dimensional conformal field theory in physics in the sense that
any result or conjecture in two-dimensional conformal field theory can
be reformulated precisely as a result or conjecture in the
representation theory of vertex operator algebras.
In this course I will present this representation theory. The topics covered will include: Weak modules, generalized modules, N-gradable weak modules and modules for a vertex operator algebra, Zhu's algebra for a vertex operator algebra, the correspondence between modules for Zhu's algebra and N-gradable weak modules for the vertex operator algebra, reductivity of N-gradable weak modules, cofiniteness conditions, intertwining operators, differential equations of regular singular points, tensor products, modular invariance, Verlinde conjecture and Verlinde formula. |