| Grant number: | 11/21621-8 |
| Support Opportunities: | Research Grants - Visiting Researcher Grant - International |
| Duration: | April 20, 2012 - June 19, 2012 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Algebra |
| Principal Investigator: | Vyacheslav Futorny |
| Grantee: | Vyacheslav Futorny |
| Visiting researcher: | Dimitar Grantcharov |
| Visiting researcher institution: | University of Texas at Arlington (UT Arlington), United States |
| Host Institution: | Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
| Associated research grant: | 10/50347-9 - Algebras, representations e applications, AP.TEM |
Abstract
The goal of this project is to study the representations theory of infinite dimensional Lie algebras and superalgebras of vector fields using localization technique. More precisely, we will focus on the category of weight modules of the Lie algebra of vector fields on an N-dimensional torus. In the case N = 1 this Lie algebra is the centerless part of the Virasoro algebra whose simple weight representations have been classified by O. Mathieu in 1992. We plan to extend some results of the breakthrough paper of Mathieu to the case of vector fields with N greater than 1. Our main tools will be the twisted localization technique developed by O. Mathieu, D. Grantcharov, and V. Serganova, as well as recent results of Y. Billig and V. Futorny about induced representations of Lie algebra of vector fields. (AU)
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