  The Hillman--Grassl correspondence is a well-known bijection between
multisets of rim hooks of a partition shape $\lambda$ and reverse plane
partitions of $\lambda$. We use the tools of quiver representations to
generalize Hillman--Grassl in type $A$ and to define an analogue in all
minuscule types. This is an extended abstract prepared for FPSAC 2019 based on
arXiv:1812.08345, emphasizing its combinatorial aspects.
