The S3 Character Table - A New Meaning - Diffusion Symmetry

Explore the concept of diffusion symmetry in this 45-minute lecture on the S3 character table. Delve into hypergroups, fusion algebras, and related systems in combinatorics, group theory, and number theory. Examine Frobenius' perspectives on characters, both as traces of irreducible representations and as functions on conjugacy classes. Investigate the hypergroup version of the S3 character table and discover a new combinatorial interpretation. Learn about irreducible representations, character tables for commutative and non-commutative groups, and the fusion rule algebra for conjugacy classes of S3. Conclude with a geometric interpretation of the hypergroup character table for S3.

Intro
Overview
Character Table of The Symmetric Group S3
Irreducible Representations of S3
Characters of Commutative Groups
Characters of Non-Commutative Groups via Representations
Definition of the Character Table of a Group
Example of Multiplying Conjugacy Classes
Fusion Rule Algebra for Conjugacy Classes of S3
The Class Hypergroup of S3
The Hypergroup Character Table for S3
A geometric Interpretation