Harmonic Analysis for Spinor Fields in Complex Hyperbolic Spaces

✍ Scribed by Roberto Camporesi

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 434 KB
• Volume: 154
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.2000.1929

✦ Synopsis

L 2 harmonic analysis for Dirac spinors on the complex hyperbolic space H n (C) is developed. The spinor spherical functions are calculated in terms of Jacobi functions. The Plancherel and Paley Wiener theorems for the spherical transform are obtained by reduction to Jacobi analysis. We demonstrate analytically the existence of harmonic L 2 spinors in the case of n even. The action of the invariant differential operators on the Poisson transforms is given explicitly. 2000 Academic Press Contents. 1. Introduction. 2. Spinors on GÂK. 3. Spinors on H n (C). 4. {-spherical functions. 4.1. Definitions and basic facts. 4.2. The differential equation. 4.3. {-spherical functions as Jacobi functions. 4.3.1. The case {={ 0 , { n . 4.3.2. The case {={ nÂ2 . 4.3.3. The generic case. 5. The spherical transform. 6. The Fourier transform. 7. The structure of the Dirac operator and of the algebras D(G, { j ).