Highest weight modules over certain quasigraded Lie algebras on elliptic curves
[For definitions and notations see the preceding review (Zbl 0820.17036).] In this paper the author studies certain representations of the higher genus affine Kac-Moody algebras. He introduces the concept of quasi-graded highest weight modules. One important observation is the fact that one should drop the assumption that there is only one highest weight vector. He studies representations which depend on 2 such vectors. It turns our that in the class of quasi-graded highest weight modules these modules can be irreducible. He shows that the modules are the direct sum of subspaces of odd resp. even parity, and that each of them has its own highest weight vector. The action of the algebra on each of these subspaces considered modulo the other subspace defines a highest weight module on it for a certain Kac-Moody algebra of genus 0. In terms of Verma modules, a classification of irreducible modules is given.
scientific article; zbMATH DE number 571846
scientific article