Intertwining Operators into Cohomology Representations for Semisimple Lie Groups

LetGbe a semisimple Lie group with finite center andLthe centralizer of a torus inG. An explicit intertwining operator is constructed from a nonunitary principal series forGinto Dolbeault cohomology onG/L. The image lies in the space of strongly harmonic forms. This paper generalizes results in (L. Barchini, A. W. Knapp, and R. Zierau,J. Funct. Anal.107(1992), 302–341) by replacing the one-dimensional fiber overG/Lwith certain Langlands quotients.