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This paper gives an explicit structure theorem for the symmetric group actingon the symmetric algebra of its natural module. Let $G$ be the symmetric groupon $x_1,..., x_n$ and let $d_i$ be the $i^{\text{th}}$ elementary symmetricpolynomial in the $x_i$'s. We show that if we take monomial representationsdiscussed in \cite[Section 3]{Kemper} to be the modules $V_I$, then we have anisomorphism of $kG$-modules $k[x_1,..., x_n] \cong \Oplus_{\{n\} \subseteq I\subseteq [n]} k[d_I] \otimes_k V_I$.

Structure Theorems for the Symmetric Groups Acting on its Natural Module