Symmetry classes of tensors associated with the Semi-Dihedral groups

TL;DR

This paper investigates the structure of symmetry classes of tensors linked to Semi-Dihedral groups, focusing on the existence of orthogonal bases of decomposable vectors and calculating their dimensions.

Contribution

It introduces the existence conditions for orthogonal bases of decomposable vectors in symmetry classes of tensors for Semi-Dihedral groups and computes their dimensions.

Findings

Existence of orthogonal bases of decomposable vectors established.

Dimensions of symmetry classes of tensors computed.

Provides foundational results for tensor symmetry related to Semi-Dihedral groups.

Abstract

We discuss the existence of an orthogonal basis consisting of decomposable vectors for some symmetry classes of tensors associated with Semi-Dihedral groups $SD_{8n}$. The dimensions of these symmetry classes of tensors are also computed.