Orthogonal bases in specific generalized symmetry classes of tensors

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Basic Sciences, Sahand University of Technology, Tabriz, Iran

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.

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References

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History

  • Receive Date: 03 October 2023
  • Revise Date: 12 January 2024
  • Accept Date: 28 January 2024

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