Classification of irreducible Harish-Chandra modules over map full toroidal Lie algebras

Abstract

A natural higher dimensional analogue of the affine-Virasoro algebra is the full toroidal Lie algebra. In this paper, we classify irreducible Harish-Chandra modules for map full toroidal Lie algebras. We show that every such module is either a cuspidal or a highest weight module. Furthermore, we prove that they turn out to be single point evaluation modules.