Lusztig polytopes and FFLV polytopes

preprint2020arXivOpen access

Abstract

In this paper we prove that in type An\tt A_n, the Feigin-Fourier-Littelmann-Vinberg (FFLV) polytope coincides with the Minkowski sum of Lusztig polytopes arising from various reduced decompositions. Using this result, we formulate a conjecture about the crystal structures on FFLV polytopes.

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