The continuous spectrum of the Dirac operator on noncompact Riemannian symmetric spaces of rank one

Camporesi, Roberto; Pedon, Emmanuel

doi:10.1090/S0002-9939-01-06294-3

The continuous spectrum of the Dirac operator on noncompact Riemannian symmetric spaces of rank one
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by Roberto Camporesi and Emmanuel Pedon PDF

Proc. Amer. Math. Soc. 130 (2002), 507-516 Request permission

Abstract:

The continuous spectrum of the Dirac operator $D$ on the complex, quaternionic, and octonionic hyperbolic spaces is calculated using representation theory. It is proved that $\operatorname {spec}_c(D)=\mathbb R$, except for the complex hyperbolic spaces $H^n(\mathbb C)$ with $n$ even, where $\operatorname {spec}_c(D)=(-\infty ,-\frac {1}{2}]\cup [\frac {1}{2},+\infty )$.

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