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

Jean-Louis Milhorat (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

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.

Domaines: Géométrie différentielle [math.DG]

Jean-Louis Milhorat. A formula for the First Eigenvalue of the Dirac Operator on Compact Spin Symmetric Spaces. Journal of Mathematical Physics, 2006, 47 (4), pp.043503, 12. ⟨hal-00004039⟩