Vertices of FFLV polytopes

Evgeny Feigin, Igor Makhlin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


FFLV polytopes describe monomial bases in irreducible representations of sln and sp2 n. 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.

Original languageEnglish
Pages (from-to)1083-1110
Number of pages28
JournalJournal of Algebraic Combinatorics
Issue number4
StatePublished - 1 Jun 2017
Externally publishedYes


  • Convex lattice polytopes
  • Degenerate flag varieties
  • FFLV polytopes
  • Monomial bases
  • PBW degenerations
  • Poset polytopes
  • Representations of semisimple Lie algebras
  • Vertex enumeration


Dive into the research topics of 'Vertices of FFLV polytopes'. Together they form a unique fingerprint.

Cite this