Joint work with David Plaza. We provide a conjecture (and the proof of the “graded degree part”) that links the Hecke category in positive characteristic and a certain “blob category” that we introduce as a quotient of KLR algebras. A part of the latter category can be understood in physical terms when the characteristic is zero. If there was a physical interpretation in the positive characteristic case, it would be majestic, because one could have physical intuition in one of the most difficult problems in representation theory (understanding the p-canonical basis).

PDF Blob algebra approach to the p-canonical basis