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Lecture
Crystallographic Coxeter Groups
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Related lectures (33)
Coxeter groups: Generators, Relations, and Word Length
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Explores Coxeter groups, word length, simple reflections, and unique elements.
Coxeter Groups: Root System Classification and Fundamental Regions
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Explains root system classification and fundamental regions in Coxeter groups.
McKay Correspondence and Coxeter Groups
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Explores the McKay correspondence, Coxeter groups, and finite subgroups of SU(2) and SO(3, emphasizing odd order properties and root system constructions.
Coxeter Groups: Geometric Equivalence and Positive Definite Graphs
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Explores the geometric equivalence of Coxeter groups with the same graph and positive definite matrices.
Coxeter Groups: Spectral Theorem and Sylvester's Criterion
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Explores the spectral theorem, Coxeter graphs, eigenvalues, and determinants of positive definite matrices.
Crystal Symmetry and Point Groups
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Covers crystal symmetry, point groups, crystal classes, and space groups in relation to crystal structures and descriptions.
Weyl character formula
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Explores the proof of the Weyl character formula for finite-dimensional representations of semisimple Lie algebras.
Isometries & Orientation in Modern Geometry
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Explores true angle magnitude, reflections, isometries, and symmetries in modern geometry, with practical CAD applications.
Simple Lie Algebras: Classification and Properties
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Explores the classification and properties of simple complex Lie algebras, emphasizing their connection with Lie groups.
Lie Algebras and Representations
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Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.
Complete Reducibility of Complex Representations
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Covers the complete reducibility of complex representations and the relation between Lie algebras and Lie groups.
Symmetry in Modern Geometry
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Delves into modern geometry, covering transformations, isometries, and symmetries.
Borcherds' Proof: Strategy
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Covers Borcherds' proof strategy, emphasizing the significance of simple roots and Weyl vectors.
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