  In this note, we prove that for the standard representation $V$of the Weyl
group $W$ of a semi-simple algebraic group of type $A_n, B_n, C_n, D_n, F_4$
and $G_2$ over $\mathbb C$, the projective variety $\mathbb P(V^m)/W$ is
projectively normal with respect to the descent of $\mathcal O(1)^{\otimes
|W|}$, where $V^m$ denote the direct sum of $m$ copies of $V$. We also prove
that for any finite group $G$ and for any finite dimentional representation $V$
over $\mathbb C$, the projective variety $P(V)/G$ is projectively normal with
respect to the descent of $\mathcal O(1)^{\otimes n!}$ as a consequence.
