Irreducible Vector and Ray Representations of Some Cubic Crystal Point Groups in Four Dimensions

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Abstract
A new, and computationally simple, method is given for obtaining the characters of all the inequivalent irreducible vector representations of a finite group. The method was applied to determine the characters of the irreducible vector and ray representations of the four‐dimensional cubic crystal point groups: group 47 and group 45. These groups are of order 384 and 1152, respectively, and contain the cubic point group in three dimensions Oh[3] as a subgroup. Tables are given of the irreducible representations of Oh subduced by the irreducible representations of group 47 and group 45. These tables may be useful in testing the conjecture that accidental degeneracy in problems in solid state physics in three dimensions reflects a higher symmetry in four dimensions.

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