Non-Symmetric Hall-Littlewood Polynomials
  Using the action of the Yang-Baxter elements of the Hecke algebra on polynomials, we define two bases of polynomials in n variables. The Hall-Littlewood polynomials are a subfamily of one of them. For q=0, these bases specialize into the two families of classical Key polynomials (i.e. Demazure characters for type A). We give a scalar product for which the two bases are adjoint of each other. 
Francois Descouens (IGM-LabInfo), Alain Lascoux (IGM-LabInfo)