Discrete groups generated by reflections
No. 147, 1974
(Algebra, group theory, mathematical theory of crystals)
India ink and pencil on paper, 30 x 43 cm.
Nearly resembling an exploding star, or an intersection of swords, this system actually represents mirrors in space, the reflections of which form a discrete group. In fact this class of groups plays a key role in geometry and physics, since some very profound questions in number theory and the theory of forms on various fields hinge on groups generated by reflections. Since a unit normal vector uniquely determines each mirror, or hyperplane, we can formulate all the properties of the group generated by reflections in terms of the set of vectors normal to the mirrors. The groups generated by reflections in mirrors in a multidimensional Lobachevsky space are especially interesting. Underlying this image is a special variety of groups, known as Weyl groups.
