On the squashed seven-sphere operator spectrum

We derive major parts of the eigenvalue spectrum operators on squashed seven-sphere that appear in compactification eleven-dimensional supergravity. These spectra determine mass fields $AdS_4$ and are important for corresponding ${\mathcal N} =1$ supermultiplet structure. This work is a continuation [1] where complete irreducible isometry representations was derived this compactification. Some comments also made concerning $G_2$ holonomy its implications structure operator equations seven-sphere.