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arXiv 2002.119992020-02math.RTmath.CO

Lusztig polytopes and FFLV polytopes

Xin Fang, Gleb Koshevoy

备注：: 22 pages, 12 figures; v2: added Proposition 5.2 and 5.4

英文摘要：

In this paper we prove that in type $\tt A_n$, 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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