Lapoint, L. Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, ChileWe work here with the linear span Λt(k) of Hall–Littlewood polynomials indexed by partitions whose first part is no larger than k. The sequence of spaces Λt(k) yields a filtration of the space Λ of symmetric functions in an infinite alphabet X. In joint work with Lascoux [4] we gave a combinatorial construction of a family of symmetric polynomials ................