Hodge theory, complex geometry, and representation theory

Hodge theory, complex geometry, and representation theory /

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Bibliographic Details
Main Author:	Green, M. (Mark)
Other Authors:	Griffiths, Phillip, 1938-, Kerr, Matthew D., 1975-
Format:	Book
Language:	English
Published:	Providence, Rhode Island : Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, [2013]
Series:	Regional conference series in mathematics; no. 118.
Subjects:	Hodge theory. Geometry, Differential. Algebraic geometry > Special varieties > Grassmannians, Schubert varieties, flag manifolds. Nonassociative rings and algebras > Lie algebras and Lie superalgebras > Cohomology of Lie (super)algebras. Topological groups, Lie groups > Locally compact groups and their algebras > Unitary representations of locally compact groups. Several complex variables and analytic spaces > Deformations of analytic structures > Period matrices, variation of Hodge structure; degenerations. Several complex variables and analytic spaces > Complex spaces with a group of automorphisms > Homogeneous complex manifolds. Algebraic geometry > Families, fibrations > Variation of Hodge structures. Algebraic geometry > Special varieties > Homogeneous spaces and generalizations. Nonassociative rings and algebras > Lie algebras and Lie superalgebras > Lie algebras of linear algebraic groups. Group theory and generalizations > Linear algebraic groups and related topics > None of the above, but in this section. Topological groups, Lie groups > Lie groups > Representations of Lie and linear algebraic groups over real fields: analytic methods. Topological groups, Lie groups > Lie groups > Semisimple Lie groups and their representations. Topological groups, Lie groups > Noncompact transformation groups > Homogeneous spaces. Several complex variables and analytic spaces > Automorphic functions > Automorphic forms. Several complex variables and analytic spaces > Holomorphic fiber spaces > Twistor theory, double fibrations. Several complex variables and analytic spaces > Complex manifolds > Stein manifolds. Differential geometry > Global differential geometry > Homogeneous manifolds.

Table of Contents:

The classical theory (2 parts)
Polarized Hodge structures and Mumford-Tate groups and domains
Hodge representations and Hodge domains
Discrete series and n-cohomology
Geometry of flag domains (2 parts)
Penrose transforms in the two main examples
Automorphic cohomology
Miscellaneous topics and some open questions.