On reduction of block matrices in a Hilbert space - Omel’chenko, P. V. (Ukrains’kyi Matematychnyi Zhurnal, 2009)
We study the problem of the reduction of self-adjoint block matrices $B = (B_ij)$ with given graph by a group of unitary block diagonal matrices. Under the condition that the matrices $B^2$ and $B^4$ are orthoscalar, we describe the graphs of block matrices for which this problem is a problem of *-finite, *-tame, or *-wild representation type.