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Extremal tensor products for Demazure crystals

Algebra & Discrete Mathematics

Speaker: Nicolle Gonzalez, UC Berkeley
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Location: 3106 MSB
Start time: Mon, Feb 6 2023, 4:10PM

Demazure models are certain Borel submodules generated by extremal weight vectors. Their crystal graphs arise as certain truncation of highest weight irreducible crystals. Extremal crystals are a broader class of subsets characterized by the so-called string condition. While all Demazure crystals are extremal, the converse is false. In recent years, Kouno gave a classification of precisely when tensor products of Demazure crystals decompose into disjoint unions of Demazure crystals. In this talk, I will explore tensor products of extremal crystals and characterize when tensor products of Demazure crystals are disjoint unions of extremal sets. In particular, these tensor products will be Demazure if and only if they are extremal, thus this characterization gives a new local criterion for when tensor products of Demazure crystals remain Demazure that differs from Kouno's global approach.

This is joint work with Sami Assaf and Anne Dranowski.