Harmonic polynomials invariant under a finite subgroup of O(n)

In this paper, an algorithm is described which allows a systematic computation of harmonic polynomials of a given degree invariant under a finite subgroup of the group O(n). An application of the algorithm to the octahedral (cubic) subgroup is given.

[1]  P. Winternitz,et al.  On bases for irreducible representations of O (3) suitable for systems with an arbitrary finite symmetry group , 1976 .

[2]  H. Puff.  Contribution to the Theory of Cubic Harmonics , 1970 .

[3]  J. Moret‐Bailly,et al.  Clebsch-Gordan coefficients adapted to cubic symmetry , 1965 .

[4]  Burnett Meyer,et al.  On the Symmetries of Spherical Harmonics , 1954, Canadian Journal of Mathematics.

[5]  A. Cracknell,et al.  Lattice Harmonics I. Cubic Groups , 1965 .

[6]  H. Bethe,et al.  A Method for Obtaining Electronic Eigenfunctions and Eigenvalues in Solids with An Application to Sodium , 1947 .

[7]  K. Fox,et al.  Construction of Tetrahedral Harmonics , 1970 .

[8]  K. Fox,et al.  COMPUTATION OF CUBIC HARMONICS , 1977 .

[9]  K. Hecht,et al.  The vibration-rotation energies of tetrahedral XY4 molecules : Part I. Theory of spherical top molecules , 1961 .

[10]  J. Killingbeck.  Integrity bases for the crystal point groups , 1972 .

[11]  D. G. Bell.  Group Theory and Crystal Lattices , 1954 .

[12]  B. G. Wybourne,et al.  Integrity bases, invariant operators and the state labelling problem for finite subgroups of SO3 , 1976 .

[13]  N. Vilenkin.  Special Functions and the Theory of Group Representations , 1968 .

[14]  M. A. Lohe,et al.  The Boson Calculus for the Orthogonal and Symplectic Groups , 1971 .

[15]  W. Döring,et al.  Die Richtungsabhängigkeit der Magnetostriktion , 1960 .

[16]  W. Burnside,et al.  Theory of Groups of Finite Order , 1909 .