On reduction of block matrices in a Hilbert space

Abstract

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.