Construction of Irreducible Coxeter Groups

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Coxeter groups: classification and crystallographic construction

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

Coxeter Groups: Simple Roots and Reflections

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

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 Theorem & Order of F_4

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

Coxeter groups: Generators, Relations, and Word Length

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

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.

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

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: Root System Classification and Fundamental Regions

Explains root system classification and fundamental regions in Coxeter groups.

Local structure of totally disconnected locally compact groups I

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.