We solve a long standing problem of the classification of all simple modules with finite-dimensional weight spaces over Lie algebra of vector fields on n-dimensional torus for any n. This generalizes the classical result of O.Mathieu on simple weight modules for the Virasoro algebra (n = 1). Every such module is either of a highest weight type or is a quotient of a module of tensor fields on a torus, which was conjectured by Eswara Rao.

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Persistent URL dx.doi.org/10.1515/crelle-2014-0059
Journal Journal fur die Reine und Angewandte Mathematik
Citation
Billig, Y, & Futorny, V. (Vyacheslav). (2016). Classification of irreducible representations of Lie algebra of vector fields on a torus. Journal fur die Reine und Angewandte Mathematik, 2016(720), 199–216. doi:10.1515/crelle-2014-0059