CRISTIAN LENART, ARTHUR LUBOVSKY
Kirillov-Reshetikhin crystals are colored directed graphs encoding the structure of certain finite-dimensional representations of affine Lie algebras. This study aims to enhance the quantum alcove model by providing a uniform realization of the combinatorial R-matrix, which serves as the unique affine crystal isomorphism permuting factors in a tensor product of KR crystals. The methodology involves generalizing Schützenberger’s sliding game for Young tableaux to all Lie types, utilizing a series of combinatorial moves identified as quantum Yang-Baxter moves. These moves are explicitly described through a reduction process to rank 2 root systems. The results indicate that the quantum alcove model retains its properties irrespective of the choice of a sequence of alcoves connecting the fundamental one to its translations, leading to a deeper understanding of the structures behind Kirillov-Reshetikhin crystals and their applications in quantum group representations.
@article{b0304fbc-580f-4e3d-91f8-598717040bab,
title={A uniform realization of the combinatori},
author={CRISTIAN LENART and ARTHUR LUBOVSKY},
year={2026},
language={en}
}TY - JOUR TI - A uniform realization of the combinatori AU - CRISTIAN LENART AU - ARTHUR LUBOVSKY PY - 2026 LA - en ER -
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