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

Abstract

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.