Coxeter groups: classification and crystallographic construction

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Related lectures (31)

Coxeter Groups: Simple Reflections and Conjugacy Log in to Mediaspace to watch this video

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

Graph Theory Basics Log in to Mediaspace to watch this video

Introduces induced flows, basis matrices, and tree solutions in graph theory.

Spanning Trees: Definition and Applications Log in to Mediaspace to watch this video

Introduces spanning trees in graphs and the Minimum Spanning Tree problem, exploring efficient algorithms for optimal decision-making.

Coxeter Groups: Simple Roots and Reflections Log in to Mediaspace to watch this video

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

Coxeter groups: reflections, rotations Log in to Mediaspace to watch this video

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

Coxeter Groups: Root System Classification and Fundamental Regions Log in to Mediaspace to watch this video

Explains root system classification and fundamental regions in Coxeter groups.

Coxeter Groups: Geometric Equivalence and Positive Definite Graphs Log in to Mediaspace to watch this video

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

Coxeter Groups: Spectral Theorem and Sylvester's Criterion Log in to Mediaspace to watch this video

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

McKay Correspondence and Coxeter Groups Log in to Mediaspace to watch this video

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)Log in to Mediaspace to watch this video

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

Conditional Statements & Graph Theory Log in to Mediaspace to watch this video

Covers conditional statements and graph theory, including proof techniques and concepts related to graphs, paths, connectivity, and gossip protocols.

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