Related papers: Hodge Representations

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…

In this thesis, I apply the Green-Griffiths-Kerr classification of Hodge representations to enumerate the Lie algebra Hodge representations of CY 3-fold type

A variation of Hodge structure is a horizontal holomorphic mapping into a flag domain D; here "horizontal" indicates that the image of the map satisfies a system of partial differential equations known as the infinitesimal period relation…

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…

For a linear algebraic group $G$ over $\bf Q$, we consider the period domains $D$ classifying $G$-mixed Hodge structures, and construct the extended period domains $D_{\mathrm{BS}}$, $D_{\mathrm{SL}(2)}$, and $\Gamma \backslash D_{\Sigma}$.…

We collect evidence in support of a conjecture of Griffiths, Green and Kerr on the arithmetic of extension classes of limiting mixed Hodge structures arising from semistable degenerations over a number field. After briefly summarizing how a…

Around 1970 Griffiths introduced the moduli of polarized Hodge structures/the period domain $D$ and described a dream to enlarge $D$ to a moduli space of degenerating polarized Hodge structures. Since in general $D$ is not a Hermitian…

We study horizontal subvarieties $Z$ of a Griffiths period domain $\mathbb D$. If $Z$ is defined by algebraic equations, and if $Z$ is also invariant under a large discrete subgroup in an appropriate sense, we prove that $Z$ is a Hermitian…

We derive a new bound on the dimension of images of period maps of global pure polarized integral variations of Hodge structures with generic Hodge datum of level at least 3. When the generic Mumford-Tate domain of the variation is a period…

This paper gives a survey on the relation between Hibi algebras and representation theory. The notion of Hodge algebras or algebras with straightening laws has been proved to be very useful to describe the structure of many important…

Let G be either SU(p,2) with p>=2, Sp(2,R) or SO(p,2) with p>=3. The symmetric spaces associated to these G's are the classical bounded symmetric domains of rank 2, with the exceptions of SO*(8)/U(4) and SO*(10)/U(5). Using the…

We study $p$-adic Hodge theory for families of Galois representations over pseudorigid spaces. Such spaces are non-archimedean analytic spaces which may be of mixed characteristic, and which arise naturally in the study of eigenvarieties at…

We present period domains of complex Hodge structures and some of their basic properties from representation theory point of view. Specifically we introduce the automorphic cohomology of period domains and the complex structure on symmetric…

We study the interpolation of Hodge-Tate and de Rham periods over rigid analytic families of Galois representations. Given a Galois representation on a coherent locally free sheaf over a reduced rigid space and a bounded range of weights,…

Mumford--Tate domains parametrize polarized Hodge structures with fixed Mumford--Tate group and play a central role in the geometry of period maps. Their degenerations are governed by nilpotent orbits and limiting mixed Hodge structures,…

In a recent paper ([1],[2]) we have classified explicitely all the unitary highest weight representations of non compact real forms of semisimple Lie Algebras on Hermitian symmetric space. These results are necessary in order to construct…

For a linear algebraic group $G$ over $\mathbf Q$, we consider the period domains $D$ classifying $G$-mixed Hodge structures, and construct the extended period domains $D_{\Sigma}$. In particular, we give toroidal partial compactifications…

This paper gives an expository account of our experiments concerning relations between modular forms for congruence subgroups of SL(3,Z) and three dimensional Galois representations. The main new result presented here is a calculation of…

We prove that, for every totally real number field E_0, there exists a weight three variation of Hodge structure of Calabi-Yau type defined over the rational numbers with associated endomorphism algebra E_0 such that the unique irreducible…

We introduce a relation on real conjugacy classes of SL(2)-orbits in a Mumford-Tate domain D which is compatible with natural partial orders on the sets of nilpotent orbits in the corresponding Lie algebra and boundary orbits in the compact…