# Codes and Expansions (CodEx) Seminar

## John Jasper (Air Force Institute of Technology)

Equi-isoclinism from symmetry

Equi-isoclinic tight fusion frames (EITFFs) are a natural generalization of equiangular tight frames (ETFs), where one-dimensional spaces, the spans of the vectors in the ETF, are replaced by r-dimensional subspaces, and projective distance is replaced by spectral distance. Much like ETFs, these objects are notoriously difficult to construct. In this talk, we look at several approaches for constructing EITFFs. We consider tight fusion frames constructed as the orbit of a single subspace under a group action. Then we use the action of a cyclic group to produce infinitely many EITFFs consisting of planes. We consider EITFFs with total symmetry, i.e., any permutation of the subspaces can be obtained by a unitary transformation. We use the representation theory of the symmetric group to construct an infinite family of totally symmetric EITFFs. Finally, we use covers of the complete graph known as DRACKNs, together with representations of the dihedral group, to construct yet another infinite family.