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Advances in Applied Clifford Algebras

, Volume 17, Issue 3, pp 537–548 | Cite as

The Generalized Dolbeault Complex in Two Clifford Variables

  • Lukáš Krump
  • Vladimír Souček
Article

Abstract.

The Penrose transform is used to construct a complex starting with the Dirac operator in two Clifford variables. The corresponding relative BGG complex and its direct image is computed for cohomology with values in line bundles induced by representations in singular infinitesimal character. The limit of the induced spectral sequence is computed in cases connected with the Dirac operator in two Clifford variables.

Mathematics Subject Classification (2000).

Primary 58J70 Secondary 30G35 

Keywords.

Generalized Dolbeault complex several Clifford variables Penrose transform 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Mathematical InstituteCharles UniversityPrahaCzech Republic

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