Confusion about notation in a paper
The notation $\delta_{i,j}$ is the Kronecker delta, a notation commonly used in physics. It's defined as:
$$\delta_{i,j} \equiv \begin{cases}1,&amp;i=j\\0,&amp;i\neq j\end{cases}$$
So, as you suspected, it's essentially a shorthand for the identity matrix.

The notation $\mathbf{S}_i \in \mathrm{R}^s$ means that each $\mathbf{S}_i$ is an $s$-dimensional vector, so the index $j$ labels the components of this vector. The term "indicator" probably refers to the concept of an indicator function, which is a function that labels some set or point with the value 1 while mapping everything else to 0. So, the "$i$-th spring indicator", in this context, is a vector that has a 1 in the $i$-th component and 0 everywhere else. That's exactly the Kronecker delta, i.e. the identity matrix.

The way this "indicator vector" gets used in equation 12 in the paper is in the form of an outer product with another vector, $\mathbf{A}_i \in \mathrm{R}^m$. The two vectors are multiplied together in the form $\mathbf{A}_i \mathbf{S}_i^{\mathrm{T}}$, which is an outer product. The result is an $m \times s$ matrix with the contents of $\mathbf{A}_i$ in the $i$-th column, and zeroes everywhere else.