Intertwining operators into cohomology representations for semisimple Lie groups II

Abstract

One approach to constructing unitary representations for semisimple Lie groups utilizes analytic cohomology on open orbits of generalized flag manifolds. This work gives explicit formulas for harmonic cocycles associated to certain holomorphic homogeneous vector bundles, extending previous results of the author (Intertwining operators into cohomology representations for semisimple Lie groups, J. Funct. Anal. 151 (1997), 138–165). The key step shows that holomorphic discrete series representations and their limits are well-behaved with respect to restriction to certain submanifolds.