Algebraic Construction of the Basis for the Irreducible Representations of Rotation Groups and for the Homogeneous Lorentz Group

The basic functions for a class of the irreducible representations of the rotation groups in n dimensions (Rn ) are explicitly constructed by an algebraic method in which the basic functions are taken to be homogeneous polynomials in the variables of En . The solutions correspond to the hyperspherical harmonics of the mathematical literature and are of interest for problems exhibiting invariance under a certain Rn . The method is also applied to derive a basis for the infinite‐dimensional irreducible representations of the homogeneous Lorentz group if we then look for homogeneous functions in the variables of the corresponding pseudo‐Euclidean space.