Sami Assaf, USC 

Title: Polo’s conjecture and products of crystals

Abstract: Demazure crystals are subsets of highest weight crystals which give a combinatorial skeleton of Demazure modules. Unlike the better known highest weight crystals, not all tensor products of Demazure crystals result in unions of Demazure crystals. This reflects the fact that not all tensor products of Demazure modules admit excellent filtrations. Polo conjectured tensor products of Demazure modules always admit superb filtrations, wherein successive quotients are Schubert modules. In this talk, we consider a new family of extremal subsets of highest weight crystals and show how they might give a crystal-theoretic model for Polo’s conjecture.