Nonlinear affine embedding of the Dirac field from the multiplicity-free SL(4, ) unirreps

The correspondence between the linear multiplicity-free unirreps of SL(4, studied by Ne'eman and Sijacki and the nonlinear realizations of the affine group is derived. The results obtained clarify the inclusion of spinorial fields in a nonlinear affine gauge theory of gravitation.