The Flag Major Index and Group Actions on Polynomial Rings
  A new extension of the major index, defined in terms of Coxeter elements, is introduced. For the classical Weyl groups of type $B$, it is equidistributed with length. For more general wreath products it appears in an explicit formula for the Hilbert series of the (diagonal action) invariant algebra. 
Ron M. Adin and Yuval Roichman