Modules with highest weight for affine Lie algebras on Riemann surfaces
In the global approach to Conformal Field Theory on higher genus Riemann surfaces initiated by Krichever and Novikov one replaces the Virasoro algebra and the related algebras by the corresponding algebras which are given by meromorphic objects with poles only at two points (see the review Zbl 0820.17036 for more background information). Starting from any simple Lie algebra \({\mathfrak g}\) (with associated group \(G)\) the generalized affine Lie algebra \(\widehat {\mathfrak g}\) was introduced by the author [Funct. Anal. Appl. 27, 266-272 (1993; Zbl 0820.17036)]. In the article under review the author defines and studies highest weight representations of these affine type Lie algebras. To study them he introduces the notion of Bloch weights which are analogs of the Bloch spectrum in the theory of completely integrable systems. An analog of the Weyl-Kac character formula is proven.
scientific article; zbMATH DE number 846563