Equi-isoclinic subspaces from symmetry

We describe a flexible technique that constructs tight fusion frames with prescribed transitive symmetry. Applying this technique with representations of the symmetric and alternating groups, we obtain several new infinite families of equi-isoclinic tight fusion frames, each with the remarkable property that its automorphism group is either Sₙ or Aₙ. These ensembles are optimal packings for Grassmannian space equipped with spectral distance, and as such, they find applications in block compressed sensing.