School of Mathematical Sciences

An insight on Modular Representation Theory of the Symmetric Group menu

An insight on Modular Representation Theory of the Symmetric Group

Speaker: 
Diego Millan Berdasco
Date/Time: 
Tue, 21/03/2017 - 12:00
Room: 
Laws 2.09

Representation Theory is one of the areas of mathematics in which a wide range of techniques can be applied, from combinatorics and differential geometry to category theory. Different abstract algebraic objects can be understood by representations of them, namely matrices (linear transformations of vector spaces). Thus, we revise the problem of studying abstract algebra into the considerably easier problem of studying linear algebra.
We will start with a quick review on the purpose and applications of Representation Theory. Following this, we will address the representations of finite groups and one of its current open problems: describe and understand the composition factors of its modular representations. Then, we will focus on the modular representation theory of S_n and an object of significant importance for its study over an arbitrary field: the Specht modules.