To constrain the last element of $S^{lo}$ equals to the first element of $S^{hi}$, if choose $L_{N-1}(X)$ as the lagrange polynomial, then $S^{hi}$ should shift to next element by times $\omega$ and get the first element of $S^{hi}$, so the equation holds
To constrain the last element of $S^{lo}$ equals to the first element of $S^{hi}$, if choose $L_{N-1}(X)$ as the lagrange polynomial, then $S^{hi}$ should shift to next element by times $\omega$ and get the first element of $S^{hi}$, so the equation holds