  The purpose of this paper is to give a reciprocity between $U_q(h)$ and $\Cal
H_{n,r}$, the Hecke algebra of $(\Bbb Z / r\Bbb Z)\wr \frak S_n$ introduced by
Ariki and Koike. Let $K=\Bbb Q(q,u_1,\dots ,u_r)$ be the field of rational
funcitons in variables $q,u_1,\dots ,u_r$. We adopt $K$ as the base field for
both the quantized universal enveloping algebra $U_q(gl_r)$ and the Hecke
algebra $\Cal H_n$. We denote by $U_q(h)$ the $K$-subalgebra of $U_q(gl_r)$
generated by $q^{E_{ii}}\;$'s $(1\le i \le r)$. In this paper, we show that the
commutant of $U_q(h)$ in $End((K^r)^{\otimes n})$ is isomorphic to a quotient
of $\Cal H_{n,r}$. We also determine the irreducible decomposition of
$(K^r)^{\otimes n}$ under the action of $\Cal H_{n,r}$. As a consequence, we
obtain the reciprocity for $U_q(h)$ and $\Cal H_{n,r}$.
