Description of a Complex of Operators Acting Between Higher Spinor Modules

  • Peter Franek
Conference paper
Part of the Trends in Mathematics book series (TM)


We construct a particular sequence of homomorphisms of generalized Verma modules and show that this sequence is a complex. The dual sequence can be identified with a complex of linear differential operators so that the first operator in this sequence is a generalization of the Dirac operator in many Clifford variables. Further, we use Zuckerman translation principle to show that a similar sequence exists for any higher spinor operator in a particular model of Cartan geometry, including, e.g., the Rarita-Schwinger operator in many variables. There are indications that this sequence may be exact, forming a resolvent of the first operator.


Differential operator complex Dirac Generalized Verma module 

Mathematics Subject Classification (2000)

22E46 32W99 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2008

Authors and Affiliations

  • Peter Franek
    • 1
  1. 1.PrahaCzech Republic

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