Lectures related to Harold Scott MacDonald Coxeter

Coxeter Groups: Classification and Exceptional Construction

Explores the classification and construction of Coxeter groups, focusing on exceptional cases and the method of inductive construction.

Coxeter Groups: Classification and Fundamental Regions

Explores Coxeter groups classification, rotation orders, fundamental regions, and geometric equivalence.

Coxeter groups: Generators, Relations, and Word Length

Explores Coxeter groups, word length, simple reflections, and unique elements.

Coxeter Groups: Reflections and Fundamental Regions

Explores Coxeter groups, reflections, fundamental regions, and classification by Coxeter graphs.

Coxeter Groups: Classification Theorem & Order of F_4

Explores the classification theorem for Coxeter groups and the order of F_4.

Coxeter Groups: Elements, Numbers, and Planes

Explores Coxeter elements, numbers, and planes in Coxeter groups with illustrative examples.

Coxeter Groups: Generators and Relations

Explores Coxeter groups, emphasizing generators, relations, and unique presentations in group theory.

Coxeter Groups: Simple Reflections and Conjugacy

Explores the theorem that an element sending all simple roots to simple roots is the identity in Coxeter groups.

Coxeter groups: classification and crystallographic construction

Covers the classification of Coxeter groups, crystallographic construction, and Coxeter elements.

McKay Graphs of Finite Subgroups of SU(2)

Explores McKay graphs for finite subgroups of SU(2) and the corresponding Coxeter graphs.

Positive Definite Coxeter Graphs

Explores the classification of positive definite connected Coxeter graphs through detailed calculations and proofs.

Eigenvalues of Coxeter Elements

Explores eigenvalues of Coxeter elements, cyclic permutations, invariance, and decomposition of eigenspaces.

Coxeter groups: reflections, rotations

Reviews Coxeter groups, reflections, rotations, and fundamental regions in finite orthogonal transformations.

Coxeter Groups: Geometric Equivalence and Positive Definite Graphs

Explores the geometric equivalence of Coxeter groups with the same graph and positive definite matrices.

Coxeter Groups: Simple Roots and Reflections

Explores the properties of simple roots and reflections in Coxeter groups, emphasizing uniqueness and linear independence.

Construction of Irreducible Coxeter Groups

Explores the construction of irreducible Coxeter groups and their geometric properties, focusing on classical and simply laced groups.

Coxeter Groups: Spectral Theorem and Sylvester's Criterion

Explores the spectral theorem, Coxeter graphs, eigenvalues, and determinants of positive definite matrices.

Coxeter Groups: Root System Classification and Fundamental Regions

Explains root system classification and fundamental regions in Coxeter groups.

Representation Theory: Finite Subgroups of SU(2)

Explores representation theory and character theory of finite groups, including scalar product and McKay graph.

McKay Correspondence and Coxeter Groups

Explores the McKay correspondence, Coxeter groups, and finite subgroups of SU(2) and SO(3, emphasizing odd order properties and root system constructions.