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arXiv · 1809.02908

On higher level Kirillov--Reshetikhin crystals, Demazure crystals, and related uniform models

Cristian Lenart·Travis Scrimshaw
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Abstract

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.

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Cristian Lenart, Travis Scrimshaw. 2019-08-27. On higher level Kirillov--Reshetikhin crystals, Demazure crystals, and related uniform models. https://doi.org/10.1016/j.jalgebra.2019.07.036

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