期刊论文详细信息
JOURNAL OF ALGEBRA 卷:539
On higher level Kirillov-Reshetikhin crystals, Demazure crystals, and related uniform models
Article
Lenart, Cristian1  Scrimshaw, Travis2 
[1] SUNY Albany, Dept Math, Albany, NY 12222 USA
[2] Univ Queensland, Sch Math & Phys, St Lucia, Qld 4072, Australia
关键词: Kirillov-Reshetikhin crystal;    Demazure crystal;    Quantum alcove model;   
DOI  :  10.1016/j.jalgebra.2019.07.036
来源: Elsevier
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【 摘 要 】

We show that a tensor product of nonexceptional type Kirillov-Reshetikhin (KR) crystals is isomorphic to a direct sum of Demazure crystals; we do this in the mixed level case and without the perfectness assumption, thus generalizing a result of Naoi. We use this result to show that, given two tensor products of such KR crystals with the same maximal weight, after removing certain 0-arrows, the two connected components containing the minimal/maximal elements are isomorphic. Based on the latter fact, we reduce a tensor product of higher level perfect KR crystals to one of single-column KR crystals, which allows us to use the uniform models available in the literature in the latter case. We also use our results to give a combinatorial interpretation of the Q-system relations. Our results are conjectured to extend to the exceptional types. (C) 2019 Elsevier Inc. All rights reserved.

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