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A nilpotent endomorphism of a quiver representation induces a lineartransformation on the vector space at each vertex. Generically among allnilpotent endomorphisms, there is a well-defined Jordan form for these lineartransformations, which is an interesting new invariant of a quiverrepresentation. If $Q$ is a Dynkin quiver and $m$ is a minuscule vertex, weshow that representations consisting of direct sums of indecomposablerepresentations all including $m$ in their support, the category of which wedenote by $\mathcal{C}_{Q,m}$, are determined up to isomorphism by thisinvariant. We use this invariant to define a bijection from isomorphism classesof representations in $\mathcal{C}_{Q,m}$ to reverse plane partitions whoseshape is the minuscule poset corresponding to $Q$ and $m$. By relating thepiecewise-linear promotion action on reverse plane partitions toAuslander-Reiten translation in the derived category, we give a uniform proofthat the order of promotion equals the Coxeter number. In type $A_n$, we showthat special cases of our bijection include the Robinson-Schensted-Knuth andHillman-Grassl correspondences.

Minuscule reverse plane partitions via quiver representations