Estudo de nova fórmula de caracteres para representações de Álgebra de Lie semissimples

• Autor(a) principal: Matías Gutierrez, Gonzalo Emanuel
• Data de Publicação: 2015
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFSCAR
• Texto Completo: https://repositorio.ufscar.br/handle/ufscar/7299
• topic: Lie Algebras; Semisimple Lie Algebras; Representations; Character; Weyl’s Formula; Character new Formula; Multiplicity Formula; Álgebras de Lie; Álgebras de Lie Semissimples; Representações; Caractere; Fórmula de Weyl; Nova Fórmula de Caracteres; Fórmula de Multiplicidades; CIENCIAS EXATAS E DA TERRA::MATEMATICA::ALGEBRA

The objective of this dissertation is descrive formally the irreducible representations of finitedimensional semisimple Lie algebras g over a field F algebraically closed with characteristic zero, as also get some multiplicity formulas that allow compute the dimension of the weight space in the representation and also the quantity of weight. In this regard, the newness of this work is the study of a new characters formula, recently published by Schützer [Sch12], and this based in one combinatory given only in terms of not simple positive roots of the Lie algebra. The main results of this dissertation are reviewed and clarified.