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Hodge Representations and Hodge Domains
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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.
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