Cuspidal representations of Lie algebras and modules finitely generated over Carta...
Vertex constructions in representation theory of infinite dimensional Lie algebra.
Representations of hyper loop algebras and equivariant map algebras
| Grant number: | 18/17955-7 |
| Support Opportunities: | Regular Research Grants |
| Start date: | January 01, 2019 |
| End date: | December 31, 2020 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Algebra |
| Principal Investigator: | Luis Enrique Ramírez |
| Grantee: | Luis Enrique Ramírez |
| Host Institution: | Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil |
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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