theory of Lie algebras, the Weyl group (named after Hermann Weyl) of a root system Φ is a subgroup of the isometry group of that root system. Specifically...

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

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

{\displaystyle T\subset K} has been chosen, one can define a root system and a Weyl group similar to what one has for semisimple Lie algebras. These structures...

Weyl group of SO(2n) is represented in SO(2n) by the preimages under the standard injection SO(2n) → SO(2n + 1) of the representatives for the Weyl group...

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...

The Weyl group is the symmetry group of an equilateral triangle, which has six elements. In this case, the Weyl group is not the full symmetry group of...

article. The Weyl group of E8, which is the group of symmetries of the maximal torus that are induced by conjugations in the whole group, has order 214 35 52 7...

isomorphism of fundamental groups, with the splitting U(1) → U(n) inducing the inverse. The Weyl group of U(n) is the symmetric group Sn, acting on the diagonal...

in the vertex algebra. The Weyl group of an affine Lie algebra can be written as a semi-direct product of the Weyl group of the zero-mode algebra (the...