A modification of the Anderson-Mirkovic conjecture for Mirkovic-Vilonen polytopes in types B and C

Abstract

We give an explicit description of the (lowering) Kashiwara operators on Mirkovi\'c-Vilonen polytopes in types $B$ and $C$, which provides a simple method for generating Mirkovi\'c-Vilonen polytopes inductively. This description can be thought of as a modification of the original Anderson-Mirkovi\'c conjecture, which Kamnitzer proved in the case of type $A$, and presented a counterexample in the case of type $C_{3}$.