A formula for the first eigenvalue of the Dirac operator on compact spin symmetric spaces

Journal Article · Sat Apr 15 00:00:00 EDT 2006 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.2186924· OSTI ID:20768765

Milhorat, Jean-Louis ^[1]

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1. Laboratoire Jean Leray, UMR CNRS 6629, Departement de Mathematiques, Universite de Nantes, 2, Rue de la Houssiniere, BP 92208, F-44322 Nantes Cedex 03 (France)

Let G/K be a simply connected spin compact inner irreducible symmetric space, endowed with the metric induced by the Killing form of G sign-changed. We give a formula for the square of the first eigenvalue of the Dirac operator in terms of a root system of G. As an example of application, we give the list of the first eigenvalues for the spin compact irreducible symmetric spaces endowed with a quaternion-Kaehler structure.

• OSTI ID: 20768765
• Journal Information: Journal of Mathematical Physics, Vol. 47, Issue 4; Other Information: DOI: 10.1063/1.2186924; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIRAC EQUATION
DIRAC OPERATORS
EIGENVALUES
SET THEORY
SPIN