A descent basis for the coinvariant algebra of type D

A monomial basis for the coinvariant algebra of type D is introduced. This basis naturally leads to the definition of a new family of representations that decompose the homogeneous components of the coinvariant algebra. Furthermore, the multiplicity of the irreducible characters within the characters of these representations is described in terms of tableaux. This algebraic setting is then applied to generalize various combinatorial identities and find new ones.