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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

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Volume 2016, Issue 720


Classification of irreducible representations of Lie algebra of vector fields on a torus

Yuly Billig / Vyacheslav Futorny
Published Online: 2014-08-19 | DOI: https://doi.org/10.1515/crelle-2014-0059


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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About the article

Received: 2013-10-15

Published Online: 2014-08-19

Published in Print: 2016-11-01

Funding Source: Conselho Nacional de Desenvolvimento Científico e Tecnológico

Award identifier / Grant number: 301743/2007-0

Funding Source: Fundação de Amparo à Pesquisa do Estado de São Paulo

Award identifier / Grant number: 2010/50347-9

Award identifier / Grant number: 2012/14961-0

The first author is supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada and by the Fapesp grant 2012/14961-0. The second author is supported in part by the CNPq grant 301743/2007-0 and by the Fapesp grant 2010/50347-9.

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2016, Issue 720, Pages 199–216, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2014-0059.

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