Séminaire Lotharingien de Combinatoire, 95B.51 (2026), 12 pp.
Joseph McDonough, Pavlo Pylyavskyy, and Shiyun Wang
Kirillov-Reshetikhin dual Equivalence Graphs
Abstract.
We introduce Kirillov-Reshetikhin dual equivalence graphs, a generalization of Assaf's dual equivalence graphs to affine type A. Given a sequence of rectangular partitions, we use commutators of adjacent crystal operators to construct a graph on the 0-weight space of the corresponding Kirillov-Reshetikhin crystal. We give a complete characterization of the set of edges that appear in these graphs, which includes standard dual equivalence moves as a subset. Furthermore, we characterize the number of connected components in terms of the energy function of the underlying crystal. We conjecture that characters of these connected components can be computed via the plethysm of cyclic characters with a product of rectangular Schur functions.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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