Coxeter Groups: Classification and Exceptional Construction

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (30)

Page 2 of 3

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: Simple Roots and Reflections

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

Coxeter groups: reflections, rotations

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

Positive Definite Coxeter Graphs

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

Coxeter Groups: Geometric Equivalence and Positive Definite Graphs

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

Crystallographic Coxeter Groups

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

Coxeter Groups: Root System Classification and Fundamental Regions

Explains root system classification and fundamental regions in Coxeter groups.

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.

Representation Theory: Finite Subgroups of SU(2)

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

Coxeter Groups: Spectral Theorem and Sylvester's Criterion

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