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Rational conformal field theories can be characterized by the property that there are, up to equivalence, finitely many irreducible representations of the vertex operator algebra, and that every representation is completely reducible.
It is tempting to relax the semisimplicity condition and study more general classes of conformal field theories. One such class are rational logarithmic conformal field theories, where not all modules are completely reducible and not even L(0) diagonalizable (here L(0) is the degree zero Virasoro generator). The main examples of LCFT come from the so-called \cal{W} vertex algebras, which play an important role in geometric Langlands theory.
In this talk we will first define several families of \cal{W}-algebras. Then we will discuss their irreducible representations and the corresponding graded dimensions (or simply, characters). Indecomposable, logarithmic modules require special care, so the notion of character will be generalized. These modified characters are in fact very useful to understand modular invariance.
Some parts of the talk are based on a joint work with D. Adamovic.
Refreshments at 4:00 pm in ES 152.