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

Benjamin Dequêne

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arXiv · 2407.13581

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

Benjamin Dequêne

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Abstract

Let $\lambda=(\lambda_1 \geqslant \ldots \geqslant \lambda_k > 0)$. For any $c$ Coxeter element of $\mathfrak{S}_{\lambda_1+k-1}$, we construct a bijection from fillings of $\lambda$ to reverse plane partitions. We recover two previous generalizations of the Robinson--Schensted--Knuth correspondence for particular choices of Coxeter element depending on $\lambda$: one based on the work of, among others, Burge, Hillman, Grassl, Knuth, and uniformly presented by Gansner; the other developed by Garver, Partrias, and Thomas, and independently by Dauvergne, called Scrambled RSK. Our results in this paper develop the combinatorial consequence of our previous work of type $A_{\lambda_1+k}$ quivers.

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Benjamin Dequêne. 2024-07-18. An extended generalization of RSK correspondence via $A$ type quiver representations. https://arxiv.org/abs/2407.13581

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