Abstract
Demazure crystals are subcrystals of highest weight irreducible \(\mathfrak {g}\)-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.
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Open access funding provided by SCELC, Statewide California Electronic Library Consortium. S. Assaf received financial support from the Simons Foundation via Simons Award SA-953878.
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Presented by: Peter Littelmann
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Assaf, S., Dranowski, A. & González, N. Extremal Tensor Products of Demazure Crystals. Algebr Represent Theor 27, 627–638 (2024). https://doi.org/10.1007/s10468-023-10231-z
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DOI: https://doi.org/10.1007/s10468-023-10231-z