Abstract
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 1-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.
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