Hypergeometric functions and the ultrahyperbolic Dirac operator

Abstract

In this article, we realize a projective model for the equivalent of the unit sphere S ^m−1⊂ℝ ^m in the orthogonal space ℝ ^{p, q} of ultrahyperbolic signature (p, q), and we define a Dirac operator on this surface within the context of the Clifford analysis. We then construct null solutions of a special type for this operator, hence obtaining a relationship between hypergeometric functions and spin-invariant systems.

Keywords:

• Clifford analysis
• Hypergeometric function
• Dirac operator
• Ultrahyperbolic space

Acknowledgements

First author was supported by F.W.O.—Vlaanderen (Belgium).