Little groups of irreps of O(3), SO(3), and the infinite axial subgroups

Details Little groups of irreps of O(3), SO(3), and the infinite axial subgroups Little groups of irreps of O(3), SO(3), and the infinite axial subgroups

2000-12-06

arxiv.org/abs/math-ph/0012008v1

Physics

Mathematical Physics

28 pages and 3 figures

Scientific paper

10.1088/0305-4470/34/34/310

Little groups are enumerated for the irreps and their components in any basis of O(3) and SO(3) up to rank 9, and for all irreps of C$_{\infty}$, C$_{\infty h}$, C$_{\infty v}$, D$_{\infty}$ and D$_{\infty h}$. The results are obtained by a new chain criterion, which distinguishes massive (rotationally inequivalent) irrep basis functions and allows for multiple branching paths, and are verified by inspection. These results are relevant to the determination of the symmetry of a material from its linear and nonlinear optical properties and to the choices of order parameters for symmetry breaking in liquid crystals.

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