Explore: Weyl Group

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

{\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

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

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

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

of a p-group, the subgroup generated by the abelian subgroups of maximal order. "Thompson subgroup" can also mean an analogue of the Weyl group used in

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

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

series groups are all simply laced, but no group of type B, C, F, or G is simply laced. Cartan matrix Coxeter matrix Weyl group Coxeter group Kac–Moody