On the stability of homogeneous Einstein manifolds II

Abstract

For any (Formula presented.) -invariant metric on a compact homogeneous space (Formula presented.), we give a formula for the Lichnerowicz Laplacian restricted to the space of all (Formula presented.) -invariant symmetric 2-tensors in terms of the structural constants of (Formula presented.). As an application, we compute the (Formula presented.) -invariant spectrum of the Lichnerowicz Laplacian for all the Einstein metrics on most generalized Wallach spaces and any flag manifold with (Formula presented.). This allows to deduce the (Formula presented.) -stability and critical point types of each of such Einstein metrics as a critical point of the scalar curvature functional.