Lecture

Eigenvalues of Coxeter Elements

In course
DEMO: occaecat culpa exercitation consectetur
Lorem amet aliquip do aute nulla enim in sit ea eu adipisicing anim. Qui laborum aliquip veniam ad occaecat reprehenderit pariatur fugiat aliqua irure do. Eiusmod eiusmod laborum esse dolor excepteur consectetur aute consequat aute eiusmod ut proident. Ea cupidatat tempor amet eiusmod ex laboris commodo aliquip. Nostrud fugiat consectetur non sunt cillum sit irure sunt minim do. Mollit excepteur cillum nulla esse minim deserunt nostrud ullamco veniam Lorem ex sunt.
Login to see this section
Description

This lecture covers the eigenvalues of a Coxeter element and the uniqueness of the Coxeter plane associated with it. It explains how any permutation among the Coxeter generators can be achieved through cyclic permutations and transpositions. The lecture also discusses the invariance of the Coxeter number and the absence of eigenvalue 1 for a Coxeter element. Additionally, it explores the relationship between the Coxeter element and its matrix, as well as the decomposition of eigenspaces. The properties of Coxeter elements, their actions as rotations in unique planes, and the projection of root systems onto the Coxeter plane are also examined.

Instructor
excepteur commodo
Ex nisi aliqua est Lorem esse laborum. Non in velit consequat consectetur consectetur. Excepteur duis ipsum dolor irure commodo fugiat non amet deserunt tempor culpa eu esse. Proident dolore commodo sunt reprehenderit enim Lorem magna sunt et occaecat officia fugiat. Nulla est id dolor non aliqua. Adipisicing do exercitation esse Lorem commodo officia deserunt incididunt ullamco proident dolore do do cillum.
Login to see this section
About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.
Ontological neighbourhood
Related lectures (35)
Coxeter Groups: Elements, Numbers, and Planes
Explores Coxeter elements, numbers, and planes in Coxeter groups with illustrative examples.
Isometries and Orthonormal Bases
Discusses isometries and orthonormal bases in mathematics.
Rotations (2D): Definitions and Analytical Expressions
Covers the concept of 2D rotations and their analytical expressions.
Physics 1: Harmonic Oscillator and Spherical Coordinates
Explores harmonic oscillators, pendulum movement, and spherical coordinates in physics.
Decay Rate & Dyson Series
Explores cross section, decay rate, and Dyson series in turbulence, emphasizing proper split and Lorentz invariance.
Show more

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.