The Lichnerowicz Laplacian on normal homogeneous spaces

We give a new formula for the Lichnerowicz Laplacian on normal homogeneous spaces in terms of Casimir operators. We derive some practical estimates and apply them to the known list of non-symmetric, compact, simply connected homogeneous spaces <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>G</m:mi> <m:mo>/</m:mo> <m:mi>H</m:mi> </m:mrow> </m:math> G/H with 𝐺 simple whose standard metric is Einstein. This yields many new examples of Einstein metrics which are stable in the Einstein–Hilbert sense, which have long been lacking in the positive scalar curvature setting.