SN - modules

• Grant number: 16/12152-8
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: October 01, 2016
• End date: September 30, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Lucio Centrone
• Grantee: Ayla Moulaz Carvalho
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The principal study of this research is the symmetric group Sn and its representations which can be couched in the language of modules. In this project, we shall study R-modules. It is important to recall that modules are a generalization of the notion of vector space, i.e., we allow scalars to be elements of R, where R is an arbitrary ring. The importance of studying modules relies is in the fact that it is equivalent to the theory of representations of groups. When we have a structure, it seems a natural problem investigating on its substructures. In particular are of interest substructures that do not contain other substructures, i.e irreducibles. In this case, modules have their substructure, otherwise known as a submodule. This project will focus on irreducible submodules which form the "building blocks" of general modules. Further, we will study the structure of Sn-irreducible modules, and finally, we shall study the Hook Formula that will count the total of such Sn-irreducible submodules.