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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 spec c (D) = R, except for the complex hyperbolic spaces H n (C) with n even, where spec c (D) = (-∞, -1/2] ∪ [1/2,+∞).

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