A formula for the First Eigenvalue of the Dirac Operator on Compact Spin Symmetric Spaces
Jean-Louis Milhorat
Abstract
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-Kähler structure.
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