Fractional conformal descendants and correlators in general 2D SN orbifold CFTs at large N

We consider correlation functions in symmetric product ($S_N$) orbifold CFTs at large $N$ with arbitrary seed CFT. Specifically, we correlators of descendant operators constructed using both the full Virasoro generators $L_{m}$ and fractional $\ell_{m/n_i}$. Using covering space techniques, show that descendants may be written entirely terms ancestors, further appropriate set ancestors are those lift to conformal primaries on cover. argue data should cancel out such calculations. To back this claim, provide some example calculations by considering a three-point function form (4-cycle)-(2-cycle)-(5-cycle) lifts cover, thereof. In these examples while is used for calculation, final descent relations do not depend data, nor details which CFT construct orbifold, making results universal.