Gelfand Pairs of Complex Reflection Groups

Abstract

In this article the zonal spherical functions of the Gelfand pair $(G(r,d,n),S_n)$ 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.

18 pages, 0 figures. Some stylistic changes have been made and the introduction now better reflects the article. Definition 3.2 and 3.3 have been fused. Minor spelling mistakes have been fixed