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Vertices of FFLV polytopes |
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| Authors: | Evgeny?Feigin |
| Institution: | 1.Department of Mathematics,National Research University Higher School of Economics,Moscow,Russia;2.Tamm Theory Division,Lebedev Physics Institute,Moscow,Russia;3.Max Planck Institute for Mathematics,Bonn,Germany;4.International Laboratory of Representation Theory and Mathematical Physics,National Research University Higher School of Economics,Moscow,Russia;5.Landau Institute for Theoretical Physics,Chernogolovka,Russia |
| Abstract: | FFLV polytopes describe monomial bases in irreducible representations of \(\mathfrak {sl}_n\) and \(\mathfrak {sp}_{2n}\). We study various sets of vertices of FFLV polytopes. First, we consider the special linear case. We prove the locality of the set of vertices with respect to the type A Dynkin diagram. Then we describe all the permutation vertices and after that we describe all the simple vertices and prove that their number is equal to the large Schröder number. Finally, we derive analogous results for symplectic Lie algebras. |
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