Classification of irreducible weight modules over higher rank Virasoro algebras

Let G be a rank n additive subgroup of C and Vir[G] the corresponding Virasoro algebra of rank n. In the present paper, irreducible weight modules with finite dimensional weight spaces over Vir[G] are completely determined. There are two different classes of them. One class consists of simple modules of intermediate series whose weight spaces are all I-dimensional. The other is constructed by using intermediate series modules over a Virasoro subalgebra of rank n - 1. The classification of such modules over the classical Virasoro algebra was obtained by O. Mathieu in 1992 using a completely different approach. (C) 2005 Elsevier Inc. All rights reserved.