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Tableaux realization of cuspidal modules for Simple Lie algebras

Abstract

This project has as main objective the explicit description of cuspidal modules for classical Lie algebras. Such modules are particular cases of weight modules with finite weight multiplicities and they exist just for Lie algebras of type $A$ and $C$. We pretend to use recent results and tools from the theory of Gelfand-Tsetlin modules (for algebras of type $A$), and develop the study of analytic continuations of the formulas that used to describe irreducible finite dimensional modules (for type $C$ algebras) with the aim of present cuspidal modules via tableaux realizations. The main advantage of this construction will be the explicit nature of the basis and action of the generators of the algebra on such basis. (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; RAMIREZ, LUIS ENRIQUE; ZHANG, JIAN. Explicit construction of irreducible modules for U-q(gl(n)). SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 13, n. 1, p. 83-95, . (15/05927-0, 14/09310-5, 18/17955-7)
FUTORNY, VYACHESLAV; GRANTCHAROV, DIMITAR; RAMIREZ, LUIS ENRIQUE. Classification of simple Gelfand-Tsetlin modules of sl(3). BULLETIN OF MATHEMATICAL SCIENCES, v. 11, n. 03, . (18/17955-7, 18/23690-6)
BENITEZ, GERMAN; RAMIREZ, LUIS ENRIQUE. Faces of polyhedra associated with relation modules. ARKIV FOR MATEMATIK, v. 60, n. 2, p. 20-pg., . (18/17955-7)
FUTORNY, VYACHESLAV; RAMIREZ, LUIS ENRIQUE; ZHANG, JIAN. Gelfand-Tsetlin representations of finite W-algebras. Journal of Pure and Applied Algebra, v. 224, n. 5, . (15/05927-0, 14/09310-5, 18/17955-7)

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