Classification of irreducible weight modules over higher rank Virasoro algebras |
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Authors: | Rencai Lu Kaiming Zhao |
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Affiliation: | a Department of Mathematics, Peking University, Beijing 100871, PR China b Institute of Mathematics, Academy of Mathematics and System Sciences, Academia Sinica, Beijing 100080, PR China c Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada N2L 3C5 d Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, PR China |
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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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Keywords: | 17B10 17B65 17B68 |
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