Orthogonal bases of Brauer relative symmetric polynomials for certain groups

Abstract

In this paper, we discuss O-basis of symmetry classes of polynomials associated with the Brauer character of the Semi-Dihedral groups and Dihedral groups. 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 Semi-Dihedral groups.