Szegِ Mappings, Harmonic Forms, and Dolbeault Cohomology

Let G/L be the quotient of a semisimple Lie Group G by the centralizer L of a torus. The author constructs an explicit intertwinig operator from derived functor modules, realized in the Langlands classification, into Dolbeault cohomology on G/L. This operator produces strongly harmonic forms. This paper generalizes the results in (L. Barchini, A. W. Knapp, and R. Zierau, J. Funct. Anal.107 (1992), 302-341) by dropping the condition real rank L = real rand G.