Eigenfunctions of MacDonald's \(q\)-difference operator for the root system of type \(C_n\) (Q1288249)

The eigenvalue problem associated with the \(q\)-difference operator introduced by Macdonald is studied. An integral representation of eigenfunctions, which is given in terms of a restriction of a \(q\)-Jordan-Pochhammer integral, is constructed for the root system of type \(C_n\). Taking a suitable cycle of the integral, the author obtains an integral representation of the Macdonald polynomial on \(C_n\) type parametrized by the partition \((\lambda,0,\dots, 0)\). It is suggested that this paper represents a step toward understanding the \(BC_n\) type Macdonald polynomials.