Intertwining operators into cohomology representations for semisimple Lie groups

Let G be a semisimple Lie group with finite center and L the centralizer of a torus in G. An explicit intertwining operator is constructed from a nonunitary principal series for G into Dolbeault cohomology on G/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 over G/L with certain Langlands quotients. (C) 1997 Academic Press.