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Special Values of Automorphic Cohomology Classes
Mark Green, University of California, Los Angeles, Phillip Griffiths, Institute for Advanced Study, Princeton, New Jersey, and Matt Kerr, Washington University in St. Louis, Missouri
cover
Memoirs of the American Mathematical Society
2014; 145 pp; softcover
Volume: 231
ISBN-10: 0-8218-9857-4
ISBN-13: 978-0-8218-9857-4
List Price: US$79
Individual Members: US$47.40
Institutional Members: US$63.20
Order Code: MEMO/231/1088
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Expected publication date is September 1, 2014.

The authors study the complex geometry and coherent cohomology of nonclassical Mumford-Tate domains and their quotients by discrete groups. Their focus throughout is on the domains \(D\) which occur as open \(G(\mathbb{R})\)-orbits in the flag varieties for \(G=SU(2,1)\) and \(Sp(4)\), regarded as classifying spaces for Hodge structures of weight three. In the context provided by these basic examples, the authors formulate and illustrate the general method by which correspondence spaces \(\mathcal{W}\) give rise to Penrose transforms between the cohomologies \(H^{q}(D,L)\) of distinct such orbits with coefficients in homogeneous line bundles.

Table of Contents

  • Introduction
  • Geometry of the Mumford Tate domains
  • Homogeneous line bundles over the Mumford Tate domains
  • Correspondence and cycle spaces; Penrose transforms
  • The Penrose transform in the automorphic case and the main result
  • Bibliography
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