Orthogonal bases of Brauer symmetry classes of tensors for groups having cyclic support on non-linear Brauer characters

TL;DR

This paper explores properties of Brauer symmetry classes of tensors, deriving a dimension formula for orbital subspaces related to non-linear Brauer characters, and investigates conditions for the existence of orthogonal bases in specific groups.

Contribution

It introduces a new dimension formula for orbital subspaces in Brauer symmetry classes of tensors for groups with cyclic support on non-linear Brauer characters.

Findings

Derived a dimension formula for orbital subspaces.

Established necessary and sufficient conditions for o-basis existence.

Provided criteria for non-vanishing elements in Brauer symmetry classes.

Abstract

This paper provides some properties of Brauer symmetry classes of tensors. We derive a dimension formula for the orbital subspaces in the Brauer symmetry classes of tensors corresponding to the irreducible Brauer characters of the groups having cyclic groups support on non-linear Brauer characters. Using the derived formula, we investigate the necessary and sufficient condition for the existence of the o-basis of Dicyclic groups, Semi-dihedral groups and also reinvestigate those things on Dihedral groups. Some criteria for the non-vanishing elements in the Brauer symmetry classes of tensors associated to those groups are also included.