Subgroups of the unitary group that contain the group of diagonal matrices

Abstract

In the group U(n,ℂ) of all complex unitary matrices we obtain a description of the lattice of those subgroups H that contain the group of diagonal unitarymatrices. This lattice is finite, and the connected intermediate subgroups H are in bijective correspondence with the equivalence relations on a set of n elements. © 1981 Plenum Publishing Corporation.