This reducible representation is decomposed into the sum of irreducible representations. A polynomial that is irreducible over any field containing the coefficients is absolutely irreducible. The total number of roots of these monic irreducible polynomials is . To any irreducible algebraic variety is associated its function field. This implies that, over , there are exactly irreducible monic polynomials of degree . Some properties of the finite irreducible Coxeter groups are given in the following table. It follows that they are roots of irreducible polynomials of degree over . There are however more types of irreducible subspaces. The theory of facilitated variation challenges irreducible complexity. States associated with these other irreducible subspaces are called parastatistic states. Young tableaux provide a way to classify all of these irreducible subspaces. He did this by only using polynomials that are irreducible over the integers. Note that the isotypes of not equivalent irreducible representations are pairwise orthogonal. In this context, the case of irreducible polynomials requires some care. For every unitary irreducible representations there is an equivalent one, .