Minuscule reverse plane partitions via quiver representations

TL;DR

This paper generalizes the Hillman--Grassl correspondence, a bijection involving reverse plane partitions, to all minuscule types using quiver representations, extending its combinatorial framework beyond type A.

Contribution

It introduces a new generalization of the Hillman--Grassl correspondence to minuscule types via quiver representations, broadening the combinatorial understanding.

Findings

Generalization of Hillman--Grassl correspondence to minuscule types

Use of quiver representations to establish the bijection

Extension of combinatorial tools beyond type A

Abstract

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.