2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116562Using 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.Dedicated to Adriano GarsiaCombinatoricsCombinatorics, Representation Theorytext