Vladimir I. Danilov, Alexander V. Karzanov, Gleb A. Koshevoy
In this work, we investigate the structure and construction of connected regular A2-crystals, specifically focusing on the crystal graphs associated with highest weight integrable modules over Uq (sl3). The primary objective is to demonstrate how such a crystal graph can be formed by taking two half-grids, replicating them, and adhering them together following a specific method. Furthermore, the paper delves into extensions of this construction and discusses related aspects that show the connections within the framework of symmetrizable quantum Kac–Moody algebras. This research contributes to the understanding of regular crystals and their implications in the field of representation theory, enhancing the mathematical framework surrounding simply-laced algebras. Results indicate that the proposed method of constructing A2-crystals yields significant insights into their properties and characterization, thus extending previous work done in the area.
@article{99c9e5b5-831f-4e54-bac5-552685ab1dc3,
title={Combinatorics of regular crystals},
author={Vladimir I. Danilov and Alexander V. Karzanov and Gleb A. Koshevoy},
year={2026},
language={en}
}TY - JOUR TI - Combinatorics of regular crystals AU - Vladimir I. Danilov AU - Alexander V. Karzanov AU - Gleb A. Koshevoy PY - 2026 LA - en ER -
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