Coxeter Groups: Classification Theorem & Order of F_4

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Isometries and Group Homomorphisms

Explores isometries, group homomorphisms, linear transformations, and group generation by similarities.

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 Reflections and Conjugacy

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

Generation and Recombination

Explores the fundamental concepts of generation and recombination in semiconductors for photovoltaic devices.

Positive Definite Coxeter Graphs

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

Coxeter Groups: Root System Classification and Fundamental Regions

Explains root system classification and fundamental regions in Coxeter groups.

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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.

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.