We generalize some identities and q-identities previously known for the
symmetric group to Coxeter groups of type B and D. The extended results include
theorems of Foata and Sch\"utzenberger, Gessel, and Roselle on various
distributions of inversion number, major index, and descent number. In order to
show our results we provide caracterizations of the systems of minimal coset
representatives of Coxeter groups of type B and D.Comment: 18 pages, 2 figure