Vladimir I. Danilov, Alexander V. Karzanov
We show that a connected regular A2-crystal (the crystal graph of an irreducible representation of sl3) can be produced from two half-grids by replicating them and gluing together in a certain way. Additionally, some extensions and related aspects are discussed. The study focuses on regular 2-colored simply-laced crystals for the Cartan matrix A2. An RC-graph can be generated from two RC-graphs of a very special form, viewed as triangular halves of two-dimensional square grids. This methodological approach clarifies the combinatorial structure of these objects, leading to significant insights into additional properties of RC-graphs and their applications.
@article{33c5b450-9562-45f3-a09e-f91c735f9c7b,
title={Combinatorics of A 2 crystals},
author={Vladimir I. Danilov and Alexander V. Karzanov},
year={2026},
language={en}
}TY - JOUR TI - Combinatorics of A 2 crystals AU - Vladimir I. Danilov AU - Alexander V. Karzanov PY - 2026 LA - en ER -
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