Weyl group

A Weyl group is a mathematical concept from the field of Lie theory, related to symmetries and structures in high-dimensional spaces. It consists of specific transformations, like reflections, that preserve certain geometric or algebraic properties within these spaces. Think of it as a set of symmetry operations that can be applied repeatedly, producing a rich pattern of arrangements. Weyl groups help mathematicians understand the structure of complex algebraic objects and are essential in areas like particle physics and geometry, providing a framework for analyzing symmetrical features in advanced mathematical systems.