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Simple Virasoro modules which are locally finite over a positive part
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2014 (English)In: Selecta Mathematica, New Series, ISSN 1022-1824, E-ISSN 1420-9020, Vol. 20, no 3, 839-854 p.Article in journal (Refereed) Published
Abstract [en]

We propose a very general construction of simple Virasoro modules generalizing and including both highest weight and Whittaker modules. This construction enables us to classify all simple Virasoro modules that are locally finite over a positive part. To obtain those irreducible Virasoro modules, we use simple modules over a family of finite dimensional solvable Lie algebras. For one of these algebras, all simple modules are classified by R. Block and we extend this classification to the next member of the family. As a result, we recover many known but also construct a lot of new simple Virasoro modules. We also propose a revision of the setup for study of Whittaker modules.

Place, publisher, year, edition, pages
2014. Vol. 20, no 3, 839-854 p.
Keyword [en]
Virasoro algebra, Simple module, Whittaker module
National Category
URN: urn:nbn:se:uu:diva-228699DOI: 10.1007/s00029-013-0140-8ISI: 000337756600006OAI: oai:DiVA.org:uu-228699DiVA: diva2:734929
Available from: 2014-07-22 Created: 2014-07-21 Last updated: 2014-07-22Bibliographically approved

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Mazorchuk, Volodymyr
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