Vladimir I. Danilov, Alexander V. Karzanov
This paper explores the combinatorial structure of regular An-, Bn-, and Cn-crystals, represented as edge-colored directed graphs. The primary objective is to discern refined structural properties of these crystals associated with representations of quantized algebras. The methodology includes studying the subcrystals of a regular An-crystal K and characterizing the intersections of maximal subcrystals based on their color classes. This investigation results in a recursive structure of K and an efficient assembly procedure. Additionally, the relationships between regular Bn-crystals and symmetric An-crystals are established using combinatorial methods. The findings not only enhance the understanding of An-crystals but also elucidate connections among different types of crystals, thereby contributing significantly to the theory of representations of Lie algebras and their quantized forms.
@article{c87d8f1c-1715-47e3-a814-92d5e08c35e6,
title={On the combinatorial structure of crysta},
author={Vladimir I. Danilov and Alexander V. Karzanov},
year={2026},
language={en}
}TY - JOUR TI - On the combinatorial structure of crysta AU - Vladimir I. Danilov AU - Alexander V. Karzanov PY - 2026 LA - en ER -
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