Extremal Tensor Products of Demazure Crystals

Demazure crystals are subcrystals of highest weight irreducible g -crystals. In this article, we study tensor products of a larger class of subcrystals, called extremal, and give a local characterization for exactly when the tensor product of Demazure crystals is extremal. We then show that tensor p...

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Bibliographic Details
Published in:Algebras and representation theory 2024-02, Vol.27 (1), p.627-638
Main Authors: Assaf, Sami, Dranowski, Anne, González, Nicolle
Format: Article
Language:English
Subjects:
Associative Rings and Algebras
Commutative Rings and Algebras
Crystals
Mathematical analysis
Mathematics
Mathematics and Statistics
Non-associative Rings and Algebras
Tensors
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Summary:Demazure crystals are subcrystals of highest weight irreducible g -crystals. In this article, we study tensor products of a larger class of subcrystals, called extremal, and give a local characterization for exactly when the tensor product of Demazure crystals is extremal. We then show that tensor products of Demazure crystals decompose into direct sums of Demazure crystals if and only if the tensor product is extremal, thus providing a sufficient and necessary local criterion for when the tensor product of Demazure crystals is itself Demazure. As an application, we show that the primary component in the tensor square of any Demazure crystal is always Demazure.
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-023-10231-z