In this article the zonal spherical functions of the Gelfand pair (G(r, d, n), Sn) of complex reflection groups will be calculated. After this, a product formula for these spherical functions and a discrete analog of the Laplace operator which has the spherical functions as eigenfunctions will be given.

中文翻译：

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复数反射群 Gelfand 对的球面函数

本文将计算复反射群 Gelfand 对 (G(r, d, n), Sn) 的纬向球函数。在此之后，将给出这些球函数的乘积公式和以球函数为特征函数的拉普拉斯算子的离散模拟。