Rodrigues formulas for the Macdonald polynomials

We present formulas of Rodrigues type giving the Macdonald polynomials for arbitrary partitions lambda through the repeated application of creation operators B-k, k=1,..., l(lambda) on the constant 1. Three expressions for the creation operators are derived one from the other. When the last of these expressions is used, the associated Rodrigues formula readily implies the integrality of the (q, t)-Kostka coefficients. The proofs given in this paper rely on the connection between affine Hecke algebras and Macdonald polynomials. (C) 1997 Academic Press.