  We analyze the centralizer of the Macdonald difference operator in an
appropriate algebra of Weyl group invariant difference operators. We show that
it coincides with Cherednik's commuting algebra of difference operators via an
analog of the Harish-Chandra isomorphism. Analogs of Harish-Chandra series are
defined and realized as solutions to the system of basic hypergeometric
difference equations associated to the centralizer algebra. These
Harish-Chandra series are then related to both Macdonald polynomials and
Chalykh's Baker-Akhiezer functions.
