Combinatorial Theory

In this paper we formulate a conjecture about the crystal structures on Feigin--Fourier--Littelmann--Vinberg (FFLV) polytopes and prove it in small rank examples. In the case of multiples of a fundamental weight this approach recovers the crystal structures defined by Kus. A key step in this approach is the realisation of FFLV polytopes as Minkowski sums of Lusztig polytopes associated to different reduced words.

Keywords: Crystal structure, Lusztig polytope, FFLV polytope.

Mathematics Subject Classifications: 05E10, 17B10