Introduction to Group Characters

This introductory text explores the theory of group characters, emphasizing their abstract structure and practical applications in science. It is designed for advanced students with a foundation in linear algebra and group theory.

Introduction to Group Characters offers a captivating exploration of the theory of group characters, highlighting how a distinct set of numbers can clarify the structure of abstract systems. This book not only delves into the theoretical aspects but also emphasizes the practical applications of group characters across various scientific disciplines, particularly where symmetry is a critical factor.

Designed for final-year undergraduates and postgraduate students, the text assumes a foundational knowledge of linear algebra and a basic understanding of group theory. It methodically explains the computation of group characters, ensuring that readers can follow along with ease. The book includes character tables for many common groups, which are either constructed within the text or provided in the exercises, all accompanied by solutions for enhanced learning.

Additionally, the chapter dedicated to permutation groups offers a thorough examination of the characters of the symmetric group, utilizing Frobenius's generating function and Schur functions. To support the main content, the book also presents supplementary material on skew-symmetric polynomials, determinants, and symmetric functions, making it a comprehensive resource. Overall, Introduction to Group Characters serves as a valuable tool for students eager to deepen their understanding of this fascinating area of algebra.