Explore: Weyl Groups

reflection group. In fact it turns out that most finite reflection groups are Weyl groups. Abstractly, Weyl groups are finite Coxeter groups, and are important

Coxeter groups include the symmetry groups of regular polytopes, and the Weyl groups of simple Lie algebras. Examples of infinite Coxeter groups include

theory of compact groups (not necessarily Lie groups and not necessarily connected) was founded by the Peter–Weyl theorem. Hermann Weyl went on to give

equation Weyl expansion Weyl fermion Weyl gauge Weyl gravity Weyl notation Weyl quantization Weyl spinor Weyl sum, a type of exponential sum Weyl symmetry:

mathematics, the Weyl character formula in representation theory describes the characters of irreducible representations of compact Lie groups in terms of

In mathematics, the Peter–Weyl theorem is a basic result in the theory of harmonic analysis, applying to topological groups that are compact, but are

orthogonal groups are algebraic groups, since the condition of preserving a form can be expressed as an equality of matrices. The name of "orthogonal group" originates

algebraically closed fields, in the classification of Weyl groups and other finite reflection groups, and in other contexts. Various properties of the Dynkin

corresponding Weyl group is called the Weyl group of G (it depends up to isomorphism on the choice of T). The first two major results about the Weyl group are as

symmetric group of permutations, the dihedral groups, and more generally all finite real reflection groups (the Coxeter groups or Weyl groups, including