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A formula for the First Eigenvalue of the Dirac Operator on Compact Spin Symmetric Spaces

Jean-Louis Milhorat
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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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Jean-Louis Milhorat. 2005-01-24. A formula for the First Eigenvalue of the Dirac Operator on Compact Spin Symmetric Spaces. https://doi.org/10.1063/1.2186924

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