Orthogonal bases in specific generalized symmetry classes of tensors

Abstract

Let $V$ be a unitary vector space. Suppose $G$ is a permutation group of degree $m$ and $\Lambda$ is an irreducible unitary representation of $G$. We denote by $V_{\Lambda}(G)$ the generalized symmetry class of tensors associated with $G$ and $\Lambda$. 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 $U_{6n}$, as well as dihedral and dicyclic groups.

Keywords

• generalized symmetry classes of tensors
• orthogonal basis
• the group $u_{6n}$
• dihedral group
• dicyclic group