Multilinear representations of rotation groups within geometric algebra

It is shown that higher-weighted representations of rotation groups can be constructed using multilinear functions in geometric algebra. Methods for obtaining the irreducible representations are found, and applied to the spatial rotation group, SO(3), and the proper Lorentz group, SO+(1,3). It is also shown that the representations can be generalized to non-linear functions, with applications to relativistic wave equations describing higher-spin particles, such as the Rarita–Schwinger equations. The internal spin degrees of freedom and the external space–time degrees of freedom are handled within the same mathematical structure.