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Teoría de representaciones de grupos finitos

 

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Author: Vargas Magán, Joaquín Eloy
Director: Narváez Macarro, Luis
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2018
Document type: Final Degree Work
Academic Title: Universidad de Sevilla. Grado en Matemáticas
Abstract: The main purpose of the Theory of Representations of finite groups is the description and classification the different representations of a finite group G. We begin with the analysis of irreducible representations, which allows us to obtain all the representations of G. To calculate them, use the Character Theory, which will help us to reduce the complexity of this problem. As part of this area, we present a series of orthogonality results and what we will call character table. Once all this is analyzed, we focus on the symmetric group more closely and its irreducible representations. We will define Young’s diagrams, the main piece for the classification of the irreducible representations of Sn. Finally, we will see some results of the Theory of Representations with more detail, such as the Schur indicator, the Frobenius formula or the Burnside Theorem. This last theorem is a result related to Group Theory in which tools of the Theory of Representations are required for their proof. El principal objetivo de la Teoría de Representaciones de grupos finitos es la descripción y clasificación de las distintas representaciones de un grupo finito G. Comenzaremos con el análisis de las representaciones irreducibles, que nos permitirá o...
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URI: https://hdl.handle.net/11441/77584

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