Orthogonal bases of Brauer relative symmetric polynomials for the the Dicyclic group

TL;DR

This paper investigates the structure of symmetry classes of polynomials related to the Brauer character of the Dicyclic group, providing conditions for orthogonal bases of symmetrized tensors.

Contribution

It introduces new criteria for the existence of orthogonal bases of symmetry classes of polynomials associated with the Brauer character of the Dicyclic group.

Findings

Necessary and sufficient conditions for orthogonal bases are established.

Conditions for the existence of standard symmetrized tensor bases are provided.

The study advances understanding of symmetry classes in relation to the Dicyclic group.

Abstract

In this paper, we discuss O-basis of symmetry classes of polynomials associated with the Brauer character of the Dicyclic group. Also, necessary and sufficient conditions are given for the existence of an orthogonal basis consisting of standard (decomposable) symmetrized tensors for the class of tensors symmetrized using a Brauer character of the Dicyclic group.