Stability of Einstein metrics on symmetric spaces of compact type

TL;DR

This paper proves the linear stability of certain symmetric spaces of compact type under the Einstein-Hilbert action, resolving the stability problem for all irreducible symmetric spaces of this type.

Contribution

It establishes the linear stability of specific symmetric spaces, namely SU(n) for n≥3 and E6/F4, completing the stability classification for irreducible symmetric spaces of compact type.

Findings

SU(n) spaces are linearly stable for n≥3

E6/F4 is linearly stable

The stability problem for all irreducible symmetric spaces of compact type is resolved

Abstract

We prove the linear stability with respect to the Einstein-Hilbert action of the symmetric spaces $\mathrm{SU}(n)$, $n\geq3$, and $E_6/F_4$. Combined with earlier results, this resolves the stability problem for irreducible symmetric spaces of compact type.