Eigenfunctions of Macdonaldʹsq-Difference Operator for the Root System of TypeCn

We construct an integral representation of eigenfunctions for Macdonaldʹsq-difference operator associated with the root system of typeCn. It is given in terms of a restriction of aq-Jordan–Pochhammer integral. Choosing a suitable cycle of the integral, we obtain an integral representation of a special case of the Macdonald polynomial for the root system of typeCn.