Description of a Complex of Operators Acting Between Higher Spinor Modules
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.
KeywordsDifferential operator complex Dirac Generalized Verma module
Mathematics Subject Classification (2000)22E46 32W99
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