For two sets of commuting variables $x=(x_1,x_2,\dots)$ and $y=(y_1,y_2,\dots)$, the identity
\begin{align*}
\prod_{i,j\ge 1}\frac{1}{1-x_i y_j}=\sum_{\lambda}s_\lambda(x)s_\lambda(y)
\end{align*}
holds as an identity of formal [power series](/page/Power%20Series) in the variables $x_i$ and $y_j$.