Special values of automorphic cohomology classes

The authors study the complex geometry and coherent cohomology of nonclassical Mumford-Tate domains and their quotients by discrete groups. Their focus throughout is on the domains D which occur as open G(\mathbb{R})-orbits in the flag varieties for G=SU(2,1) and Sp(4), regarded as classifying spaces for Hodge structures of weight three. In the context provided by these basic examples, the authors formulate and illustrate the general method by which correspondence spaces \mathcal{W} give rise to Penrose transforms between the cohomologies H^{q}(D,L) of distinct such orbits with coefficients in homogeneous line bundles.