Given two sets of variables $Y=\{y_1,\cdots,y_n\}$, $Z=\{z_1,\cdots,z_m\}$, and two partitions $\lambda$ and $\mu$. Is there a formula for the product of the Schur functions $s_{\lambda}(Y) s_{\mu}(Z)$?
If $Y=Z$ then the answer is given by the Littlewood–Richardson rule, but what if they are not the same?