I found this notation in a published article, with no formal definition. I am attaching a screenshot of where it's used.
where, $i,l \in \mathcal{N}$.
I am guessing $\mathbf{1}_{\{i=l\}}$ denotes a vector of all zeroes, except a one at index $i=l$. This is because $\frac{\partial S_i}{\partial P_l}$ would be $1$ for $i=l$ (as per the equation), while $0$ otherwise. Is this correct?