Relative symmetry classes of polynomials, Orthogonal $*$- basis


In this note, the existence of orthogonal ∗-basis of the symmetry classes of polynomials is discussed. Analogously to the orthogonal ∗-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.

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