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Eigenfunctions of Macdonald's $q$-difference operator for the root system of type $C_n$

Katsuhisa Mimachi
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Abstract

We construct an integral representation of eigenfunctions for Macdonald's $q$-difference operator associated with the root system of type $C_n .$ It is given in terms of a restriction of a $q$-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 type $C_n .$

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Katsuhisa Mimachi. 1997-12-25. Eigenfunctions of Macdonald's $q$-difference operator for the root system of type $C_n$. https://arxiv.org/abs/q-alg/9712054

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