Variations of Hodge structure and orbits in flag varieties

Period domains, the classifying spaces for (pure, polarized) Hodge structures, and more generally Mumford-Tate domains, arise as open GR-orbits in flag varieties G/P. We investigate Hodge-theoretic aspects of the geometry and representation theory associated with these flag varieties. In particular, we relate the Griffiths-Yukawa coupling to the variety of lines on G/P (under a minimal homogeneous embedding), construct a large class of polarized GR-orbits in G/P, and compute the associated Hodge-theoretic boundary components. An emphasis is placed throughout on adjoint flag varieties and the corresponding families of Hodge structures of levels two and four.