Demazure crystals decompose naturally into subsets called Demazure atoms. We derive a recursive formula for computing Demazure atoms, generalizing a result of Lascoux and Schützenberger, and further study subsets of crystals which exhibit similar atom-positive decompositions. In particular, a conjecture of Polo suggests that the tensor product of Demazure crystals should be atom-positive. Recent work by Assaf, Dranowski, and González uncovers a relationship between Polo's conjecture and particular subsets called extremal crystals, and we further examine the relationship between extremal crystals and atom-positivity.
Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.
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Meeting ID: 915 4733 5974