Representation Theory of W
نویسنده
چکیده
We study the representation theory of the W -algebra Wk(ḡ) associated with a simple Lie algebra ḡ at level k. We show that the “−” reduction functor is exact and sends an irreducible module to zero or an irreducible module at any level k ∈ C. Moreover, we show that the character of each irreducible highest weight representation of Wk(ḡ) is completely determined by that of the corresponding irreducible highest weight representation of affine Lie algebra g of ḡ. As a consequence we complete (for the “−” reduction) the proof of the conjecture of E. Frenkel, V. Kac and M. Wakimoto on the existence and the construction of the modular invariant representations of W -algebras.
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