@article{oai:aue.repo.nii.ac.jp:00004824,
 author = {Abe, Yoshikazu and Hattori, Chuichiro and Ito, Masato and Matsuda, Masahisa and Matsunaga, Mamoru and Matsuoka, Takeo},
 issue = {6},
 journal = {Progress of theoretical physics},
 month = {},
 note = {text, In the four-dimensional effective theory from string compactification discrete flavor symmetries arise from symmetric structure of the compactified space and generally contain both the R symmetry and non-R symmetry. We point out that a new type of non-Abelian flavor symmetry can also appear if the compact space is non-commutative. Introducing the dihedral group D_4 as such a new type of flavor symmetry together with the R symmetry and non-R symmetry in SU(6)×SU(2)_R model, we explain not only fermion mass hierarchies but also hierarchical energy scales including the breaking scale of the GUT-type gauge symmetry, intermediate Majorana masses of R-handed neutrinos and the scale of μ-term.},
 pages = {1275--1295},
 title = {Flavor symmetry on non-commutative compact space and SU(6) x SU(2)_R model.},
 volume = {106},
 year = {2001}
}