Orthogonal $*$-basis of relative symmetry classes of polynomials

Abstract

In this note, the existence of orthogonal â-basis of the symmetry classes of polynomials is discussed. Analogously to the orthogonal â-basis of symmetry classes of tensor, some criteria for the existence of the basis for finite groups are provided. A condition for the existence of such basis of symmetry classes of polynomials associated to symmetric groups and some irreducible characters is also investigated.