  In an earlier work, we proved that MV polytopes parameterize both Lusztig's
canonical basis and the Mirkovic-Vilonen cycles on the Affine Grassmannian.
Each of these sets has a crystal structure (due to Kashiwara-Lusztig on the
canonical basis side and due to Braverman-Finkelberg-Gaitsgory on the MV cycles
side). We show that these two crystal structures agree. As an application, we
consider a conjecture of Anderson-Mirkovic which describes the BFG crystal
structure on the level of MV polytopes. We prove their conjecture for sl_n and
give a counterexample for sp_6. Finally we explain how Kashiwara data can be
recovered from MV polytopes.
