Intertwining operators between line bundles on Grassmannians

Let G=GL(n,F) where F is a local field of arbitrary characteristic, and let $\pi_1,\pi_2$ be representations induced from characters of two maximal parabolic subgroups $P_1,P_2$. We explicitly determine the space $Hom_G(\pi_1,\pi_2)$ of intertwining operators and prove that it has dimension at most 1 in all cases.