The Aizenbud-Lapid binary operation for symmetrizable Cartan types

Abstract

Aizenbud and Lapid recently introduced a binary operation on the crystal graph $B(-\infty )$ associated to a symmetric Cartan matrix. We extend their construction to symmetrizable Cartan matrices.

arXiv comment16 pages, based on master thesis, comments welcome. V2:Added a rigidity assumption to the cancellation property. This was necessary to fix an error in the proof