Orthogonal bases in specific generalized symmetry classes of tensors

Let V be a unitary vector space. Suppose G is a permutation group of degree m and Λ is an irreducible unitary representation of G. We denote by VΛ(G) the generalized symmetry class of tensors associated with G and Λ. In this paper, we prove the existence of orthogonal bases consisting of generalized decomposable symmetrized tensors for the generalized symmetry classes of tensors associated with unitary irreducible representations of group U6n, as well as dihedral and dicyclic groups.