Search engine for discovering works of Art, research articles, and books related to Art and Culture
Javascript must be enabled to continue!
Hodge Representations and Hodge Domains
View through CrossRef
This chapter deals with Hodge representations and Hodge domains. For general polarized Hodge structures, it considers which semi-simple ℚ-algebraic groups M can be Mumford-Tate groups of polarized Hodge structures, the different realizations of M as a Mumford-Tate group, and the relationship among the corresponding Mumford-Tate domains. The chapter uses standard material from the structure theory of semisimple Lie algebras and their representation theory. The discussion covers the adjoint representation and characterization of which weights give faithful Hodge representations, the classical groups and the exceptional groups, and Mumford-Tate domains as particular homogeneous complex manifolds. The examples concerning the classical groups illustrate both the linear algebra and Vogan diagram methods.
Princeton University Press
Title: Hodge Representations and Hodge Domains
Description:
This chapter deals with Hodge representations and Hodge domains.
For general polarized Hodge structures, it considers which semi-simple ℚ-algebraic groups M can be Mumford-Tate groups of polarized Hodge structures, the different realizations of M as a Mumford-Tate group, and the relationship among the corresponding Mumford-Tate domains.
The chapter uses standard material from the structure theory of semisimple Lie algebras and their representation theory.
The discussion covers the adjoint representation and characterization of which weights give faithful Hodge representations, the classical groups and the exceptional groups, and Mumford-Tate domains as particular homogeneous complex manifolds.
The examples concerning the classical groups illustrate both the linear algebra and Vogan diagram methods.
Related Results
Charles Hodge, Hermeneutics, and the Struggle with Scripture
Charles Hodge, Hermeneutics, and the Struggle with Scripture
Abstract
Charles Hodge continues to garner interest in contemporary theology, though sometimes for unlikely ends. This article assesses one example of this interest....
Mumford-Tate Groups
Mumford-Tate Groups
This chapter provides an introduction to the basic definitions and properties of Mumford-Tate groups in both the case of Hodge structures and of mixed Hodge structures. Hodge struc...
Autoinhibition of cMyBP-C by its middle domains
Autoinhibition of cMyBP-C by its middle domains
AbstractCardiac myosin binding protein-C (cMyBP-C) is a sarcomere regulatory protein consisting of 11 well-folded immunoglobulin-like (Ig-like) and fibronectin type-III domains wit...
Hodge–Dirac, Hodge-Laplacian and Hodge–Stokes operators in $L^p$ spaces on Lipschitz domains
Hodge–Dirac, Hodge-Laplacian and Hodge–Stokes operators in $L^p$ spaces on Lipschitz domains
This paper concerns Hodge–Dirac operators
D_{{}^\Vert}=d+\underline{\delta}
acting in
L^p(\Omega, ...
The Hodge filtration of a monodromic mixed Hodge module and the irregular Hodge filtration
The Hodge filtration of a monodromic mixed Hodge module and the irregular Hodge filtration
For an algebraic vector bundle E over a smooth algebraic variety X, a monodromic D-module on E is decomposed into a direct sum of some O-modules on X. We show that the Hodge filtra...
Meta-Representations as Representations of Processes
Meta-Representations as Representations of Processes
In this study, we explore how the notion of meta-representations in Higher-Order Theories (HOT) of consciousness can be implemented in computational models. HOT suggests that consc...
Multidomain Proteins
Multidomain Proteins
Abstract
Protein domains that have a necessary function are often used in many different proteins. Protein architecture has evolved to utilise a...
Hodge and generalized Hodge conjectures, coniveau and algebraic cycles
Hodge and generalized Hodge conjectures, coniveau and algebraic cycles
This is a survey of the Hodge conjecture, with emphasis on its companion, the generalized Hodge conjecture, which involves the theory of Hodge structures, algebraic cycles and moti...