Representation Theory of Finite Groups

Abstract

This thesis explores the representation theory of finite groups, focusing on their structure and ap- plications. It begins with group theory fundamentals, including subgroups and normal subgroups,

then transitions to linear algebra concepts like inner product spaces and unitary operators. The core

discusses linear representations, irreducibility, and Maschke’s theorem, which decomposes represen- tations into irreducible components. Character theory and orthogonality relations are analyzed,

along with representations of symmetric groups using Young tableaux. Practical examples, such as character tables and the Frobenius formula, illustrate key ideas.