CARTESIAN SYMMETRY CLASSES ASSOCIATED WITH CERTAIN SUBGROUPS OF Sm

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 Sm (generated by a product of disjoint cycles) and the product of cyclic subgroups of Sm 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.