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 $\spec_c(D)=(-\infty,-{1\over 2}]\cup [{1\over 2},+\infty)$
Publié le : 2002-07-05
Classification:
Hyperbolic spaces,
Spinors,
Dirac operator,
Spectral theory,
MSC 43A85, 58J50,
[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT],
[MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP]
@article{hal-00160420,
author = {Pedon, Emmanuel and Camporesi, Roberto},
title = {The continuous spectrum of the Dirac operator on noncompact Riemannian symmetric spaces of rank one},
journal = {HAL},
volume = {2002},
number = {0},
year = {2002},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00160420}
}
Pedon, Emmanuel; Camporesi, Roberto. The continuous spectrum of the Dirac operator on noncompact Riemannian symmetric spaces of rank one. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00160420/