This monograph presents topics in Hodge theory and representation theory, two of the most active and important areas in contemporary mathematics. The underlying theme is the use of complex geometry to understand the two subjects and their relationships to one another--an approach that is complementary to what is in the literature. Finite-dimensional representation theory and complex geometry enter via the concept of Hodge representations and Hodge domains. Infinite-dimensional representation theory, specifically the discrete series and their limits, enters through the realization of these representations through complex geometry as pioneered by Schmid, and in the subsequent description of automorphic cohomology. For the latter topic, of particular importance is the recent work of Carayol that potentially introduces a new perspective in arithmetic automorphic representation theory. The present work gives a treatment of Carayol's work, and some extensions of it, set in a general complex geometric framework. Additional subjects include a description of the relationship between limiting mixed Hodge structures and the boundary orbit structure of Hodge domains, a general treatment of the correspondence spaces that are used to construct Penrose transforms and selected other topics from the recent literature. A co-publication of the AMS and CBMS.
Hodge Theory, Complex Geometry, and Representation Theory: NSF-CBMS Regional Conference in Mathematics, June 18, 2012, Texas Christian University, Fort Worth,...
Organized around the basic concepts of variations of Hodge structure and period maps, this volume draws together new developments in deformation theory, mirror symmetry, Galois representations, iterated integrals, algebraic cycles and the ...
Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains.
Mumford-Tate groups are the fundamental symmetry groups of Hodge theory, a subject which rests at the center of contemporary complex algebraic geometry. This book is the first comprehensive exploration of Mumford-Tate groups and domains.
It is the first of three volumes dedicated to p-adic Hodge theory. This proceedings volume contains articles related to the research presented at the 2017 Simons Symposium on p-adic Hodge theory.
This book is based on lectures given at the Graduate Summer School of the 2015 Park City Mathematics Institute program “Geometry of moduli spaces and representation theory”, and is devoted to several interrelated topics in algebraic ...
0< r
This collection of surveys present an overview of recent developments in Complex Geometry.
Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.
This is a version of the Jacobson— Morosov theorem. EXERCISE A.3.7 Let N C g[(V) be nilpotent and Y C g[(V) be semisimple. Set V4 I E4 Then the following are equivalent: (1) There exists an slg—triple {N+, NI, Y} with N+ I N. (2) The ...