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We give a new formula for the Lichnerowicz Laplacian on normal homogeneousspaces in terms of Casimir operators. We derive some practical estimates andapply them to the known list of non-symmetric, compact, simply connectedhomogeneous spaces $G/H$ with $G$ simple whose standard metric is Einstein.This yields many new examples of Einstein metrics which are stable in theEinstein-Hilbert sense, which have long been lacking in the positive scalarcurvature setting.

The Lichnerowicz Laplacian on normal homogeneous spaces