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 $Ho{m}_G({\pi }_1,{\pi }_2)$ of intertwining operators and prove that it has dimension at most 1 in all cases.