MULTILINEAR REPRESENTATIONS OF ROTATION GROUPS WITHIN GEOMETRIC ALGEBRA

It is shown that higher-weighted representations of rotation groups ca n be constructed using multilinear functions in geometric algebra. Met hods for obtaining the irreducible representations art:found, and appl ied to the spatial rotation group, SO(3), and the proper Lorentz group . SO+(1,3). It is also shown that the representations can be generaliz ed to non-linear functions, with applications to relativistic wave equ ations describing higher-spin particles, such as the Rarita-Schwinger equations, The internal spin degrees of freedom and the external space -time degrees of freedom;ire handled within the same mathematical stru cture. (C) 1998 American Institute of Physics.