Representations of sl(3, IR) with half-integral spin bands

A series of irreducible representations of sl(3,IR) is constructed with half-integral spin bands which parallels the principal series of SL(3,IR). While the principal series for SL(3,IR) was shown by Weaver and Biedenharn to be applicable to even–even deformed nuclei, the series constructed here applies to odd mass nuclei. It is shown how parity is included in an SL(3,IR) algebraic model. A second (cuspidal parabolic) series of representations of SL(3,IR) is constructed, which is required for the harmonic analysis of wave functions on SL(3,IR), a necessary preliminary to the application of the results of the SL(3,IR) model in a full microscopic treatment of deformed nuclei. It is shown that the cuspidal parabolic series has undesirable properties for the description of collective states in rare-earth nuclei.