Intertwining operators into Dolbeault cohomology representations (Q1193912)

Let \(G\) be a linear connected semisimple real Lie group with the complexification \(G^ C\), let \(K\) be a maximal compact subgroup in \(G\) and let \(T\) be a torus in \(K\) with \(L\) the centralizer of \(T\) in \(G\). The authors assume that \(G\) and \(L\) have the same real rank. Unitary irreducible representations of \(G\) can be obtained on the space of Dolbeault cohomology sections of a holomorphic line bundle over \(G/L\). The authors give a nonzero integral intertwining operator from derived functor modules, realized in the Langlands classification, to the Dolbeault cohomology representation.