Zeros of covariant vector fields for the point groups : invariant formulation
- 1 January 1984
- journal article
- Published by EDP Sciences in Journal de Physique
- Vol. 45 (1), 1-27
- https://doi.org/10.1051/jphys:019840045010100
Abstract
All finite as well as infinite (matrix) point subgroups of full orthogonal groups in two and three dimensions are considered. For each point group a polynomial integrity basis for invariants and the basic polynomial vector fields are first given. Then, the strata are defined via equations and inequalities involving the integrity basis. Finally, equations for zeros of a covariant vector field are given on each stratum in terms of the integrity basis, which appears via coefficients in the expansion of the vector field on the vector-field basis. All the results are tabulated and an illustration using the cubic group is presented. Mathematical background sufficient for extensions of the results is also givenKeywords
This publication has 15 references indexed in Scilit:
- Spontaneous symmetry breaking and the chain criterionPhysical Review B, 1981
- Symmetry defects and broken symmetry. Configurations Hidden SymmetryReviews of Modern Physics, 1980
- Invariants of finite groups and their applications to combinatoricsBulletin of the American Mathematical Society, 1979
- Polynomial irreducible tensors for point groupsJournal of Mathematical Physics, 1978
- Relative invariants of finite groups generated by pseudoreflectionsJournal of Algebra, 1977
- New algorithms for the Molien functionJournal of Mathematical Physics, 1977
- Smooth functions invariant under the action of a compact lie groupTopology, 1975
- Fine structure in the optical absorption edge of anisotropic crystalsJournal of Physics and Chemistry of Solids, 1960
- Finite Unitary Reflection GroupsCanadian Journal of Mathematics, 1954
- The product of the generators of a finite group generated by reflectionsDuke Mathematical Journal, 1951