Group Theory

Playlist 1.1 Matrix functions
Matrices : 2 kinds (10 min) 1.2 Matrix functions
Derivative of a matrix function (4 min) 1.3 Matrix functions
Exponential, logarithm of a matrix (7 min) 1.4 Matrix functions
Determinant is a volume (8 min) 1.5 Matrix functions
log det = tr log (8 min) 1.6 Matrix functions
Multi-matrix functions (10 min) 1.7 Matrix functions
Linear differential equations (9 min) 1.8 Eigenvalues and eigenvectors
Projection operators (14 min) 1.9 Eigenvalues and eigenvectors
What's the deal with Hamilton-Cayley? (4 min) 1.10 Eigenvalues and eigenvectors
Spectral decomposition (4 min) 1.11 Eigenvalues and eigenvectors
Spectral decomposition and completeness (4 min) 1.12 Eigenvalues and eigenvectors
Right, left eigenvectors (6 min) 1.13 Eigenvalues and eigenvectors
A projection operators workout (9 min)

Playlist Dresselhaus et al Chapter 1 Basic Mathematical Background Cvitanović et al Chapter 10. Flips, slides and turns Discrete symmetry, an example:
3-disk pinball (4:03 min) What is a group? (10:56 min) Socratica
group multiplication (or Cayley) tables (7:32) Active, passive coordinate transformations (3:08 min) Following Mefisto:
symmetry defined three (3) times (7:01 min) Subgroups, classes, group orbits (7:57 min)

Playlist Dresselhaus et al Chapter 2 Representation Theory and Basic Theorems This requires character (1:23 min) Hard work builds character (15:05 min)
The symmetry group of a propeller (6:13 min)
Irreps of C_3 (14:52 min)
Rotation and reflections in a plane: irreps of D_3 (13:38 min)

Playlist Dresselhaus et al Sect. 2.4 The Unitarity of Representations Dresselhaus et al Sects. 2.5 and 2.6 Schur's Lemma Lecture 3 (Unedited)
Unitarity of reps; Schur's Lemma (2:04:56 h)

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Playlist Dresselhaus et al Sect. 2.7 `Wonderful' Orthogonality Theorem, sect. 2.8 Representations and vector spaces 4.2 Whence "orthogonality"?
The ideas: observables are Hermitian; matrix reps are unitary; average over the group to extract invariants. A matrix rep forms a complex unit vector, hence "orthogonality". (9:47 min) 4.3 Character orthogonality theorem (XX min) Dresselhaus et al Sect. 3.1 Characters and Class to sect. 3.5 The number of irreducible representations 4.4 Characters. Character orthogonality (XX min) 4.5 Class (17:56 min) 4.6 Number of classes equals the number of irreps (6:24 min)

Irreps (3:09 min) Frobenius character formula (12:04 min) Character orthogonality relations (10:53 min) A summary
it is all about class and character (18:50 min)

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Playlist Lecture 12 Lie groups, algebras (Unedited) (2:20:50 min)

Playlist Lecture 13 O(2) symmetry sliced (Unedited) (2:13:38 min)

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