q-Eulerian Polynomials Arising from Coxeter Groups

We study the polynomials obtained by enumerating a finite Coxeter group by number of descents. The type A case gives rise to the familiar Eulerian polynomials, while the B and D cases provided two new q -analogues. Various recursion relations, generating functions and unimodality properties are derived, which generalize and unify earlier results of Dolgachev, Lunts, Stanley and Stembridge.