Generation of spatially periodic structures consisting of superimposed atomic slates.

Abstract

We give a systematic discussion of the relation betweensubsingular vectors of Vema modules over semisimple tie algebras F and differential equations which are conditionally 5invariant. This is extended t o~t h e Drinfeld-limbo q-deformation Uq(G) of G. We treat in detail the conformal algebra su(2, Z), its complexification rI(4) and their q-deformations. The conditionally invariant equations are the d' Alembert equation and a new equation arising from a subsingular vector proposed by Bemstein-Gel'fand-GeI'fand. We also give the q-difference analogues of these equations.