Irreducible (m)-modules of Hermitean monogenics

Abstract

We study spaces of spinor-valued polynomial solutions for the Hermitean Dirac operators, obtained by projecting the classical Dirac operator on the eigen-spaces of a complex structure J. In this way, explicit realizations for specific (m)-modules are obtained.

Keywords:

• Hermitean Clifford analysis
• Young diagrams

AMS Subject Classifications:

• 30G35
• 43A65
• 15A66

Acknowledgements

The author wants to thank Professor Vladimir Souček from the Department of Mathematics and Physics at Charles University (Prague) for his kind hospitality and the fruitful discussions during the year he was able to spend at Charles University, supported by an FWO mobility grant.

Notes

Note

1. The author is a postdoctoral fellow supported by the FWO-Vlaanderen.