Cartesian symmetry classes associated with certain subgroups of S_m

In this paper, the problem existing O-basis for Cartesian symmetry classes is discussed. The dimensions of Cartesian symmetry classes associated with a cyclic subgroup of the symmetric group S_m (generated by a product of disjoint cycles) and the product of cyclic subgroups of S_m are explicitly expressed in terms of the Ramanajun sum. Additionally, a necessary and sufficient condition for the existence of an O-basis for Cartesian symmetry classes associated with the irreducible characters of dihedral group is given. The dimensions of these classes are also computed.

کلیدواژه ها:

Irreducible characters ، Cartesian symmetry classes ، orthogonal basis ، cyclic group ، Dihedral group ، Ramanujan sum