We present an explicit difference operator diagonalized by the Macdonald
polynomials associated with an (arbitrary) admissible pair of irreducible
reduced crystallographic root systems. By the duality symmetry, this gives rise
to an explicit Pieri formula for the Macdonald polynomials in question. The
simplest examples of our construction recover Macdonald's celebrated difference
operators and associated Pieri formulas pertaining to the minuscule and
quasi-minuscule weights. As further by-products, explicit expansions and
Littlewood-Richardson type formulas are obtained for the Macdonald polynomials
associated with a special class of small weights.Comment: 11 pages. To appear in Int. Math. Res. Not. IMR
