Sam Armon, USC

Abstract: Demazure crystals decompose naturally into subsets called Demazure atoms. We derive a recursive formula for computing Demazure atoms, generalizing a result of Lascoux and Sch\"{u}tzenberger, and further study subsets of crystals which exhibit similar atom-positive decompositions. In particular, Polo's conjecture states that the tensor product of Demazure crystals should be atom-positive. Recent work by Assaf, Dranowski, and Gonz\'{a}lez 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.