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## Vertices of FFLV polytopes

arxiv.org. math. Cornell University, 2016. No. arXiv:1604.08844 .
FFLV polytopes describe monomial bases in irreducible representations of sln. We study various sets of vertices of FFLV polytopes. First, we prove the locality of set of vertices with respect to the type A Dynkin diagram. Second, we describe all the permutation vertices. Third, we describe all the simple vertices and prove that their number is equal to the large Scr\"oder number. Finally, we derive analogous results for symplectic algebras.