An extended generalization of RSK correspondence via $A$ type quiver representations

Let $λ=(λ_1 \geqslant \ldots \geqslant λ_k > 0)$. For any $c$ Coxeter element of $\mathfrak{S}_{λ_1+k-1}$, we construct a bijection from fillings of $λ$ to reverse plane partitions. We recover two previous generalizations of the Robinson--Schensted--Knuth correspondence for particular choices of Cox