Analogues of the Dolbeault Complex and the Separation of Variables

  • Vladimír Souček
Chapter
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 144)

Abstract

The Dirac equation is an analogue of the Cauchy-Riemann equations in higher dimensions. An analogues of the \( \bar \partial \) operator in the theory of several complex variables in higher dimensions is the Dirac operator D in several Clifford variables. It is possible to construct a resolution starting with the operator D, which is an analogue of the Dolbeault complex. A suitable tool for studying properties of this resolution is the separation of variables for spinor valued fields in several vector variables and the corresponding Howe dual pair, which is of independent interest.

Key words

Generalized Dolbeault complex several Clifford variables separation of variables Howe pairs 

AMS(M0S) subject classifications

Primary 30G35 32W99 58J10 
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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Vladimír Souček
    • 1
  1. 1.Mathematical InstituteCharles UniversitySokolovská 83Czech Republic

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