Permutation representations, epikernels and phase transitions

Abstract

The subgroups that arise in phase transitions from a high-symmetry phase are characterized as those subgroups that are maximal with respect to the property of acting trivially on a given non-zero subspace Ui of the representation space Mi of a given irreducible representation Ti of H. In the case of subgroups of finite index the problem is reduced to that of studying faithful irreducible representations of finite groups. The use of permutation representations considerably simplifies the theory. Tables of the equitranslation epikernels of the space groups are given.