2016/06/14 by Ana-Maria Brecan, Brecan, Ana-Maria
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1606.04555
openalex publication_date 2016/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Flag domains are open orbits of real semisimple Lie groups in flag manifolds of their complexification. A special class of flag domains constitute the classifying spaces for variations of Hodge structure, namely period domains or more generally Mumford-Tate domains. In this paper we classify all proper, equivariant embeddings of a flag domain of Hodge type, required to satisfy a certain transversality condition, in a period domain and show that any such flag domain must be a Hermitian symmetric space of non-compact type of classical type. In particular, the classification describes also the proper, equivariant embeddings of a flag domain of Hodge type in a period domain satisfying Griffiths transversality.