Representations of quantum affine algebras

Abstract

Let @ be a finite dimensional simple Lie algebra and @ the corresponding affine Kac-Moody algebra. The notion of the fusion in the category (9 of representations of a n n e Kac-Moody algebras (5 was introduced ten years ago by physicists in the framework of Conformal Field Theory. This notion was developed in a number of mathematical papers (see, for example, [TUY]) where the notion of fusion is rigorously defined and in [D1] where the relation between the fusion and quantum groups in the quasi-classical region was established. This line of development was extended in [KL] to a construction on equivalence between the "fusion" category for an arbitrary negative charge and the category of representations of the corresponding quantum group (for simply-laced affine Kac-Moody algebras).