Publication date:
31 July 2017
Source:Advances in Mathematics, Volume 315
Author(s): Matt Kerr, Colleen Robles
Period domains, the classifying spaces for (pure, polarized) Hodge structures, and more generally Mumford–Tate domains, arise as open $G_{\mathbb{R}}$-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 $G_{\mathbb{R}}$-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.