Cristian Lenart, Adam Schultze
We biject two combinatorial models for tensor products of (single-column) Kirillov-Reshetikhin crystals of any classical type A − D: the quantum alcove model and the tableau model. This allows us to translate calculations in the former model (of the energy function, the combinatorial R-matrix, etc.) to the latter, which is simpler. By establishing an explicit bijection, we facilitate the use of tableau models in computations traditionally dominated by the quantum alcove model. This translates the computational efficacy of the latter into a more accessible combinatorial framework of the tableau model, making it valuable for researchers working with Kac-Moody algebras and quantum groups. The research concludes that while both models serve distinct purposes, the bijection offers a promising pathway for integrating the computational strengths of both models, thereby enriching the study of affine crystals.
@article{bc262440-afc3-4513-a2af-a104e84a924b,
title={On Combinatorial Models for Affine Cryst},
author={Cristian Lenart and Adam Schultze},
year={2026},
language={en}
}TY - JOUR TI - On Combinatorial Models for Affine Cryst AU - Cristian Lenart AU - Adam Schultze PY - 2026 LA - en ER -
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