Séminaire Lotharingien de Combinatoire, 89B.12 (2023), 11 pp.

Sami Assaf, Anne Dranowski and Nicolle González

Extremal Tensor Products of Demazure Crystals are Direct Sums of Demazure Crystals

Abstract. We give a new necessary and sufficient condition for when tensor products of Demazure crystals decompose as direct sums of Demazure crystals. Our local criterion depends on the string property which Demazure crystals, and more generally, extremal crystals, exhibit. Our characterization implies that tensor products of Demazure crystals are direct sums of Demazure crystals if and only if they are extremal.

Received: November 15, 2022. Accepted: February 20, 2023. Final version: April 1, 2023.

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