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Representations of Lie (super)algebras of vector fields

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


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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Scientific publications (4)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
FUTORNY, VYACHESLAV; GRANTCHAROV, DIMITAR; RAMIREZ, LUIS ENRIQUE. Singular Gelfand-Tsetlin modules of gl(n). ADVANCES IN MATHEMATICS, v. 290, p. 453-482, . (11/21621-8, 14/09310-5, 12/23450-9)
FUTORNY, VYACHESLAV; GRANTCHAROV, DIMITAR; MAZORCHUK, VOLODYMYR. WEIGHT MODULES OVER INFINITE DIMENSIONAL WEYL ALGEBRAS. Proceedings of the American Mathematical Society, v. 142, n. 9, p. 3049-3057, . (10/50347-9, 11/21621-8)
FUTORNY, VYACHESLAV; GRANTCHAROV, DIMITAR; RAMIREZ, LUIS ENRIQUE. Irreducible Generic Gelfand-Tsetlin Modules of gl(n). Symmetry Integrability and Geometry-Methods and Applications, v. 11, . (11/21621-8, 14/09310-5, 12/23450-9)
FUTORNY, VYACHESLAV; GRANTCHAROV, DIMITAR; MARTINS, RENATO A.. Localization of Free Field Realizations of Affine Lie Algebras. LETTERS IN MATHEMATICAL PHYSICS, v. 105, n. 4, p. 483-502, . (12/02459-8, 11/21621-8, 14/09310-5)

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