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

摘要

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) =(-infinity, -1/2] boolean OR [1/2, +infinity). [References: 12]