Coxeter Groups: Simple Reflections and Conjugacy

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

Explores Coxeter groups classification, rotation orders, fundamental regions, and geometric equivalence.

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Explores the properties of p-subgroups of Sylow in a group.

Explores the local structure of totally disconnected locally compact groups and their isomorphisms through conjugation.

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

Explores eigenvalues of Coxeter elements, cyclic permutations, invariance, and decomposition of eigenspaces.