
Lecture Description
Representation Theory of Finite Groups: We compute the character tables of S5, the symmetric group on 5 letters, and A5, the subgroup of even permutations. We note that A5 is isomorphic to the group of rigid motions of an icosahedron.
Course Index
- RT1: Representation Theory Basics
- RT2: Unitary Representations
- RT3. Equivalence and Examples (Expanded)
- RT4.1. Constructions from Linear Algebra (Expanded)
- RT4.1.1: Complex Conjugate Representations
- RT4.2. Schur's Lemma (Expanded)
- RT5. Mostly Exercises (Expanded)
- RT6. Representations on Function Spaces
- RT7.1: Finite Abelian Groups: Character Orthogonality
- RT7.2. Finite Abelian Groups: Fourier Analysis
- RT7.3. Finite Abelian Groups: Convolution
- RT8.1. Schur Orthogonality Relations
- RT8.2. Finite Groups: Classification of Irreducibles
- RT8.3. Finite Groups: Projection to Irreducibles
- RT9. Basic Tensor Analysis
- RT9.1. Application of Tensors: Normal Modes
- Character Tables for S4 and A4
- Character Tables for S5 and A5
Course Description
Doctor Bob provides 18 short video lectures on the introduction to representation theory. Group representations are where group theory meets linear algebra, and important applications arise in various math subjects (number theory, analysis, algebraic geometry), physics, and chemistry.
We consider the basic representation theory of finite groups. Goals include a look at Fourier series/analysis using groups and elementary character theory.
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