Coxeter Groups: Elements, Numbers, and Planes

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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.

Crystallographic Coxeter Groups

Explores crystallographic Coxeter groups, lattice preservation, and the classification of irreducible Weyl groups.

Coxeter groups: reflections, rotations

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

Coxeter Groups: Simple Roots and Reflections

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

Coxeter Groups: Root System Classification and Fundamental Regions

Explains root system classification and fundamental regions in Coxeter groups.

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: Spectral Theorem and Sylvester's Criterion

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

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.