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Symmetries and Overdetermined Systems of Partial Differential Equations pp 1–24Cite as

Overdetermined Systems, Conformal Differential Geometry, and the BGG Complex

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Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 144))

Abstract

This is an expanded version of a series of two lectures given at the IMA summer program “Symmetries and overdetermined systems of partial differential equations”. The main part of the article describes the Riemannian version of the prolongation procedure for certain overdetermined systems obtained recently in joint work with T.P. Branson, M.G. Eastwood, and A.R. Gover. First a simple special case is discussed, then the (Riemannian) procedure is described in general.

The prolongation procedure was derived from a simplification of the construction of Bernstein-Gelfand-Gelfand (BGG) sequences of invariant differential operators for certain geometric structures. The version of this construction for conformai structures is described next. Finally, we discuss generalizations of both the prolongation procedure and the construction of invariant operators to other geometric structures.

Supported by project P15747-N05 of the “Fonds zur Förderung der wissenschaftlichen Forschung” (FWF) and by the Insitute for Mathematics and its Applications (IMA).

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Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, A-1090, Wien, Austria

    Andreas Čap

  2. International Erwin Schrödinger Institute for Mathematical Physics, Boltzmanngasse 9, A-1090, Wien, Austria

    Andreas Čap

Authors
  1. Andreas Čap
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, The University of Adelaide, SA, 5005, Australia

    Michael Eastwood

  2. School of Mathematics, University of Minnesota, 127 Vincent Hall, 206 Church St. SE, Minneapolis, MN, 55455

    Willard Miller Jr.

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Čap, A. (2008). Overdetermined Systems, Conformal Differential Geometry, and the BGG Complex. In: Eastwood, M., Miller, W. (eds) Symmetries and Overdetermined Systems of Partial Differential Equations. The IMA Volumes in Mathematics and its Applications, vol 144. Springer, New York, NY. https://doi.org/10.1007/978-0-387-73831-4_1

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