Subgroups of the unitary group that contain the group of diagonal matrices
In the groupU(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 ofn elements.
Unable to display preview. Download preview PDF.
- 1.Z. I. Borevich, “A description of the subgroups of the full linear group that contain the group of diagonal matrices,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst. Akad. Nauk SSSR,64, 12–29 (1976).Google Scholar
- 2.Kh. D. Ikramov, A Book of Problems in Linear Algebra [in Russian], Nauka, Moscow (1975).Google Scholar