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Cuspidal representations of Lie algebras and modules finitely generated over Cartan subalgebra

Grant number: 22/05915-6
Support Opportunities:Scholarships abroad - Research Internship - Doctorate
Effective date (Start): August 22, 2022
Effective date (End): June 21, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal Investigator:Iryna Kashuba
Grantee:Eduardo Monteiro Mendonça
Supervisor: Olivier Mathieu
Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Research place: Université Claude Bernard Lyon 1, France  
Associated to the scholarship:20/14313-4 - Cuspidal Representations of Lie Algebras, BP.DR

Abstract

The goal of this project is to study combinatoric aspects of irreducible cuspidal representations of a simple lie algebra g and their relation with g-modules that are finitely generated by the universal envelop algebra of h, a fixed Cartan sub algebra of g. Cuspidal representation was classified by Olivier Mathieu, that also gave a formula for their weight spaces dimensions. We intend to refine his description with a combinatoric point of view, and that way obtain a formula of such dimensions only with positive coefficients. Furthermore, we have as second goal to study the weighting functor, the functor that map a g-module of finite type over U(h) to a weight module. By studying tensor modules, we hope to construct a inverse functor to the weighting functor. (AU)

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