An attempt is made to find an analog, for the quantum mechanics of non-Euclidean space-time, to the classification of representations of the Lorentz group. The difficulty of obtaining any such classification in terms of curvilinear coordinates is pointed out, and the use of a higher-dimensional set of pseudo-Euclidean coordinates is chosen as an alternative mode of attack. A class of representations then follows easily. On the basis of an intuitive approximation it is found that spectra of elementary particles, with conservation of quantities of the nature of isotopic spin, seem to arise from these representations.

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