  We study the effect of spin injection into a Luttinger liquid. The
spin-injection-detection setup of Johnson and Silsbee is considered; here spins
injected into the Luttinger liquid induce, across an interface with a
ferromagnetic metal, either a spin-dependent current ($I_s$) or a
spin-dependent boundary voltage ($V_s$). We find that the spin-charge
separation nature of the Luttinger liquid affects $I_s$ and $V_s$ in a very
different fashion. In particular, in the Ohmic regime, $V_s$ depends on the
spin transport properties of the Luttinger liquid in essentially the same way
as it would in the case of a Fermi liquid. The implications of our results for
the spin-injection-detection experiments in the high $T_c$ cuprates are
discussed.
